Luckily this discussion gets to bypass most of the wooden wand problem since it is hard to enchant something into smoke!
How do others feel on smoke as a minor magical focus or a minor potent magic? Smoke from natural fires, smoke created by CrAu, fancy smoke such as incense. Certainly some Au, Im, and Me effects mostly although I can see a at least the potential for other spells such that effect things wreathed in the smoke which is where it gets touchy.
Rego spells that push things or drive them off (smoking out vermin or animals)
Rego spells that use incense as purification that drives off or wards against spirits
Muto spells that change an object by wreathing it in magic smoke
Smoke as a preservative implies some CrAn effects that probably aren't a big deal but could be a nice thematic touch if you create a ritual spell or enchant an item to act as a smokehouse
If this was being used as a potent magic could the spell be written with an Ig requisite so that you could have a small amount of special wood or incense on you that the spell ignited to create the necessary smoke? For example cedar gives +5 to mentum effects. Could you have a small splint of cedar wood on you that the potent spell ignites into cedar smoke that then give a PeMu effect of erasing the last few minutes of memory in the target? The other, much weaker, option would seem to be needing to physically sprinkle the sawdust onto a small ember or coal in a jar.
Related but a separate question - are there any tricks in how potent magic interacts with flexible formulaic magic? I don't see any although I assume that the flexibility can not change anything about the potent portion of the spell.
A Magical Focus provides a bonus for magic that affects things within its scope. IMHO, many of the things you mention would not fall within the scope of a focus in smoke.
Taking your examples:
Rego spells that push or move things through a supernatural effect does not affect the smoke. Creating some smoke that naturally drive things off is not Rego magic, since creating smoke is simply CrAu. If may or may not drive vermins or animals away, depending on the intensity or the smoke itself and the propensity of said animals to be driven off by smoke. But a focus with smoke would not apply to a ReAn effect. (See below for an exception*)
Same thing with ReVi or ReMe to drive off or ward against spirits. Smoke is simply fluff, so a focus with smoke would not provide any benefit. (See below for an exception*)
Same thing with a Muto effect to transform an object. That would be MuAn, MuHe, MuTe or something like it. Smoke is just a cosmetic effect. (See below for an exception*)
Creating smoke to help preserve food might work under the focus. In the same way that magical fire can cook food permanently, even if the fire is just temporary, magical smoke should definitively be able to induce the preservation effect on food. But you are simply creating the smoke with CrAu. The smoking process is natural.
Now, a case could be made that it is possible to apply a focus with smoke when creating/transforming smoke with some magical properties and using it to affect something else. But that is a fairly high-level effect, which would start with the MuAu guideline "Base 10: Transform an amount of air into something wholly unnatural." and tack on several requisites (with added magnitudes). And such a spell would (and should) be less efficient then a normal spell.
So creating a smoke that drives off magical spirits would start with CrAu with a Mu requisite at Base 15 (creating smoke with unnatural properties), then adding Re and Vi requisites (+2 magnitudes). This would have the same effectiveness as a base ReVi effect, but would affect an area of effect based on how much smoke is created. Add R:Touch (+1 magnitude) and at least D:Conc (+1 magnitude), and you now have a Individual amount of smoke that can ward against magical spirits which have Might less than the (level of the spell - 7 magnitudes). Doable but not very efficient.
That's really why I listed those effects separately; I didn't think they should apply as a focus. Then again it's not exactly the same but also isn't completely different from getting the benefits for a focus in wolves just because you enchanted a wolf bone wand to cast a completely non-wolf related spell and some people seem to be ok with that.
On the other hand it is a shame if you can't somehow manage to use potent magic with the material bonuses from incense (different woods, amber, myrrh and so forth) in any way that is different from merely holding it in hand. Holding a spirit in place by burning a stick of incense while moving in a circle leaving a a barrier that could be broken by focused wind but not be scratched out by a sword feels so much more thematic than merely inscribing a circle on the ground with a piece of incense (wood) in your hand. Magically cleansing a room with incense that fills all the corners feels better than standing in the middle of the room holding the incense.
Slightly different discussion that is not meant to be a rules issue.
In your example inefficient spell you state CrAu with a Mu requisite at Base 15 because it is smoke with unnatural properties. Yet if you can use the shape and materials effects there are things used as incense (and woods that are used in incense) that have the property of effecting spirits or demons. For these it seems like a natural property assuming that one can bring out the property using potent magic or some other method.
Do correspondences such as the material bonus exist in the universe whether or not a mage is around (even if the bonuses aren't changing anything) or does the will of the magician force the universe to see the correspondence because the mage believes it is there? I haven't thought deeply on it but in the same fashion as saying the lion is the king of the beasts is a true belief in a Mythic Europe setting I would say that iron is harmful to faeries, an apple is a particularly healthful fruit, and ash wood is harmful to people are true statements. Without a magical or supernatural ability to make use of the connection it might not matter but it is present and real.
These properties may exist independently of the magus, but they are only brought to bear for a magus who has Potent Magic, and then only in the form of a bonus. But by themselves they are not strong enough to produce a magical effect.
Given that it seems that they are part of the essential nature of the objects which implies, to me at least, that you don't need Mu if you can create specific smoke. Since you can CrTe copper or iron into existence it is clear that the magic can differentiate if the mage cares to design the spell that way.
Just an interesting side thought that I don't think should effect anything mechanically in the game other than perhaps an occassional Mu requisite.
If you're creating a smoke that doesn't exist in the real world, then you need to add the Muto, because in the process of creating it, you're turning it into a an highly unusual smoke.
Also, since Muto has a high guideline (level 10), then technically, the spell proposed above would be Mu(Cr, Re)Au(Vim)35
(Base 10, Muto +1, Rego +1, Vim +1, Touch +1, Concentration +1)
For game mechanical purposes I agree with what I think you are saying; a cleansing smoke against spirits doesn't work without magic so it needs muto to change the air into smoke. It might also need creo to create the smoke although I'd have to think about it some more and look at already existing spells to see whether the creation or the change is actually the most important thing.
It still bums me out that there seems to be no reasonable way to use the material bonuses from burning incense through potent magic.
It also feels odd that the only response leans into the tight interpretation of foci when most of the discussions in past threads has leaned into the broad version of things such as sword, wolves, and wooden wands. I rather like the tight interpretation as I think it leads to better stories but I have enough of a gamer in me to chafe at things that far apart and inconsistent in a point buy system.
Edit
Right before posting this I was looking up something else and came across Curse of the Evil Humors (MuAu 25, R Voice, D Diam, T Part) that changes air into a "foul humors that cause disease." This seems to be support for the idea that you only need Mu and not Cr to bring about an area of gaseous effects that is inline with the Mythic Europe paradigm.
Note that the spell turns air into causing disease. But you're speaking about a smoke focus. You could skip the Cr if you cast your spell on an existing smoke, but if there's no existing smoke, you'd either need to cast a spell to make one, or cast a version with the Creo requisite, to create an unnatural one.
I take it that you are making a distinction between smoke and foul humors such that air and foul humors are in one category of things under Aurum such that you can change between them while smoke is a separate category that can not magically change into air or foul humors even with muto magic. Makes sense I guess although I'd want to look at a lot more published spells before saying which is the most correct reading.
I'd happily play using either interpretation although if I was going to play an Aurum specialist I'd certainly want to hash it out a little before playing!
If a MuAu(Te) spell could turn stone into smoke, a spell to turn air into smoke would be MuAu(Au) which... that's just a MuAu spell. Pretty sure no Creo is required.
Sure, you can do that, it's still a very inefficient way of repelling supernatural creatures, since you need to chanfe the air into smoke, and you're left as a spell that affects Magnitude -6 if Arthur's calculation is correct, so your level 30 Mu(Re)Au(Vim) spell is as efficient as a ReVi5 spell...
Sometimes I feel this is the most singled minded group! I think we are all in agreement that RAW means that no matter whether it is Mu, Cr, or some combo of one with requisite of the other it would be an ineffectual way to create the effect I initially mentioned.
I'm not really worried about the specifics of warding / cleansing with such a spell now. I'm much more interested in at least attempting to get some insight into how others rule on some things that are unclear and perhaps even inconsistent. Erik found the exact type of precedent that I knew I'd seen but couldn't put my hand on. He also phrased in it a very nice game mechanical method with the idea of MuAu (Mu) which simplifies to MuAu.
The question of how or if you can get a game mechanical difference between holding myrrh versus burning myrrh as incense while at the same type making the difference between myrrh, cedar, and sandalwood (for instance) matter is a different question and perhaps I should start a different thread.
Having had a chance to read some more what I'm looking for is rather like the Rustic Magi Spell Foci virtue although I was really only thinking of it effecting formulaic spells not spontaneous ones. Which leads a a question about what craft would be used? Or is it like Potent Magic and only needs someone with Spell Foci to create the spell assigning the specific material component? But that doesn't jibe with the mention of spontaneous magic in the text?
From a powergaming point of view this doesn't seem particularly bad especially as there are very few canonical material bonuses for things that make good incense (the various woods, myrrh, frankincense, perhaps a few more)
Thematically it fits very nicely as I'm thinking of a Criamon who walks the Path of Walking Backwards and becomes a mystical chef at the third initiation. The idea had been bouncing around as chef, tea master, or incense master with the initial thought being that incense would be connected to his gift and later his experience with Enigmatic Wisdom and understanding harmony would allow him to expand from incense to other smells and tastes or perhaps just stay with blending perfectly artistic incense blends.