Can't have a familiar with a soul

Yes, I handled that. That was the reason for the ritual and then acting to maintain the trust. There is no coercion at this point. You have altered who you're trying to get to bond with you from how they had been, but there is no coercion at all since you're acting to keep their trust and they are free to choose otherwise.

Certainly sounds fine to me.

RoP:I disagrees with you on p.29!
At least as far as demons are concerned; though if demons have souls, the same should hold for angels.

Yes, but it doesn't say humans who are fae, but humans who become fae, which suggests a becoming as opposed to faerie blood or the like.

Also ROP:I does not say that demons have souls. It states that damned souls which return to earth are counted amongst the terrestrial demons (which means these are souls rather than having them) but being counted amongst is not the same as being. In no other place I could find does it even suggest that demons have souls.

Is it actually mentioned, in any of the books, that a human loses their soul when they become a magical being?

It's mentioned repeatedly that "characters with a Might score are not human, strictly speaking." (see e.g. RoP:I, p.84).
But nowhere does it say explicitly that this means not having a soul.
Which is a somewhat fuzzy concept in terms of game mechanics anyway; you explicitly do not need to have a soul to possess (a Magical Quality that replicates all the effects of) the Gift, for example.

Sure. That's why I said "It doesn't specify how Warped or whatever they need to be, though." I was suggesting Warping as a possible process while saying the process might be something else and isn't specified. Still, the point is it is referring to people who don't have might but have become fay. They're not truly beings of faeries; they're still people, and they can be bound.

I have been wanting to get a character to bind a Great Beast (a Bjornaer mage after Final Twilight) as a Familiar.
So many story implications. But I hadn't thought about the soul aspect before.

If you follow Augustine or Thomas Aquinas, both (HoH:MC p.24) Great Beast and small animal have souls: animal souls, that is.

If you follow the somewhat anachronistic, but consistent usage of the word in A&A p.31, both don't have souls: 'soul' there refers to 'intellectual soul' in the sense of Thomas Aquinas, and thereby roughly follows modern usage. TC p.28 Care of Souls refers to 'cura animarum', a term from Church Law for the appointment of priests, not connected to any philosophical definition of 'soul'.

Cheers

Is having a soul a mechanical function of Ars Magica? Or is it more an abstract issue dependent upon each individual saga?

yes

To which part? And if it is a mechanical function of Ars, do you have a reference as to where it's classified?

Core rules page 103: A familiar is a beast that the magus befriends and then magically bonds with.
I submit that a beast and a human are differente things, or equivalently that humans are not beasts.
Therefore humans can not be bound as familiars.

Certain virtues allow for faeries to be familiars or indeed spirits. This makes faeries and spiritis exceptions.

RoP:Infernal has input on demon familiars.
Demons can also be bound but only as long as the are beasts.
A demonic dog yes, A demon seductress whose form is human no. (My interpretation of the above statement)

I believe that a Bjornaer passed into final twillight has become a beast. Although I do not imagine such a beast wanting to become a familiar.
I believe that this is discussed somewhere but I am unsure as to the source.

I don't disagree that a beast and a human being are different things. But the discussion here is on the concept of bonding a familiar who has a soul, and my question was whether or not souls are a mechanical construct of Ars or if that's a "ysmv" issue.

In the core 5th edition rulebook, "The limit of the Soul" is one of the lesser limits of Hermetic magic on page 80, and may be a special case of the limit of the Divine or may be a flaw in Hermetic magic. The spell "Lay to rest the haunting spirit" and "Exchange of the two minds" make clear that they don't affect souls in their action. The church section on page 202-3 gives a little background but points out areas of theological uncertainty.

Really, "The limit of the Soul" is the game mechanic to say "No tinkering with souls without a massive magical breakthrough or use of Divine/Infernal powers" and the deeper reasoning and minor technicalities depends on your view of souls, philosophy and theology and which medieval thinker you want to go with.

In addition to what others have said and reinforcing what darkwing just wrote, take a look at CrAn and CrCo guidelines for raising the dead in the core book. Combine that those with the first sentence on the Limit of the Soul: "Hermetic magic cannot create an immortal soul, and so may not create true human life nor restore the dead to life." I don't have the background to make any arguments on types of souls, just back up how the term is being used here.

And how about the "people" exception made available by a Virtue?

And yet neither of these explicitly answers the question I put forth: Is the soul a mechanical function of Ars? If so, I'd like to see a reference to a book and page where it is stated that only human beings have souls, and that you can only bond familiars that don't have a soul.

What we showed is not that only human beings have souls. Rather, we showed that animals do not have souls. (Again, not getting into soul types, just going by core "soul.") In the core rules you bond animals, and animals don't have souls. So are souls mechanically present? Yes.

However, there are places in the rules where they are quite clear that they are being vague about what happens to the soul when certain things happen to the individual. In that regard, certainly ysmv.

You can bond demons, spirits more generally, and people with the appropriate Virtues. That certainly leaves some availability of bonding something with a soul.

RoP:M p83 states that nobody knows if Magical Humans have souls.
ArM5 p80 explicitly states that Demons and Angels are souls.

If you need a virtue to bind a demon, then I guess you need a virtue to bind anything else with a soul.
Unless, the virtue has nothing to do with souls, it lets you bind Infernal Might rather than Magic Might. Which virtue in RoP:I is it? I can only find references to the Famulus...