My take on cognizant/semi-cognizant and the role of story is that it is very advance knowledge of Faerie nature. One can have a high level in Faerie lore that covers vast knowledge of myths, legends, faerie types, weakness and strength, but not necessarily an insight into ture Faerie nature and the role of stories in a Faerie existence. This is something so obscure, even alien - it is akin of metagame knowledge within Mythic Europe.
If you want to introduce the full Faerie concept, I would propose you a short campaign in three steps, ideally with PC who don't know much about faerie. It will allow them (and you) to get acquainted progressively with Faeries, stories and the concept of cognizant:
Base story: a farmer with a nice orchard comes to the covenant: "Master, a strange thing is happening to my apple trees. Ya see, instead of becoming, nice, fat apples, they are scrawny, and look. like that." He then put on the table three of such apples, the size of big walnut, brownish-green, wrinkled. And when looking closer, it looks like a kind of "folded" crab. And suddenly, the crab stretches its claws, more legs sprout/unfold and the little bugger starts to run away.
After research/analysis, the mages find out that the orchard is probably being claimed by the Knight of Claw & Fruit, a faerie. The whole orchard is falling under his control and his power is akin to a faerie curse. It is difficult to dispel, but there is a non-magical way to get rid of the Knight's curse.
If the Knight is defeated, his helmet (the shape of crab shell) can be used to brew a potion that can be used to lift the curse and the claim set by the Knight.
However, the Knight is a powerful foe in combat, his shell-armor seems to protect him well against mundane attack as well as magical spells, even bouncing back some of them. The PCs might lose their first fight.
More research will let them discover that the Crab-knight armor is very sensitive to apple-cider vinegar (which is "rotten" apple juice, the anti-thesis of nice, healthy apples), so if the Crab-knight is doused with apple-cider vinegar, his resistance, his armor will melt away, turning him into an easier foe to fight.
(I let you stats the Crab-knight according to your character strength, but ideally, it is an adventure for young mages, powerful mages should be able to overcome even the enhance protection of the Knight, just by their raw power).
First adventure - Discovering faerie
The purpose is to have the characters discover in-game faeries, as antagonist.
Run the scenario as summarized. Ideally, a faerie lore of 2-3 would help find leads to some cues and solution of the problem. Do not introduce the concept of cognizant faerie yet, just use faeries as regular protagonist. Allow the character who did most of the research/experiment related to faerie, faerie curse to get a nice boost of faerie lore XP, maybe to the next level. NPCs characters can help with finding the cure, the weakness.
Second adventure, a few years later - Discovering recurring stories
A farmer, from another village, or better a Redcap coming from several villages away talked about strange apple turning to small crabs.
It is so specific, that the mages have little doubt that it is the a similar case, if not the same one. When they investigate, every thing looks similar, except the look of the crab is different, it looks more like a crayfish, the name of the Knight is the Knight of Shell and Bloom. He looks different, but still close enough to the other knight. Him or his armor have a scar or a hole where the final blow was given.
And the solution is the same. Exactly the same. The adventure should be much easier to solve than the first time, because they are a few years older and they already know what to do. And to their surprise, it works perfectly. The knight is flustered, even frustrated that he is being dispatch so easily! To the point that as the final blow is given to the Knight, he might let go "But how did you know ? Did we already fight ? I feel deprived..." and then expires.
Now, open the door to the faerie specialist to dig into more obscure faerie lore tome to discover the concept of stories, giving glimpse of what is the nature of a fae and their needs for human interaction as character. Understanding that by jumping to the conclusion is like reading the first and last chapters of the story, bypassing all the others chapters, leading to a boring, short story. Most NPCs will only be able to offers info on curses and solutions, but only one or two would confirm that, yes, there are recurring stories, it is in fact more common than what people thing, but it is hard to fathom why.
Third adventure, a few years later, or even just the following year - becoming an actor-accomplice
The faerie expert might be looking to test his understanding - it could be a way to get initiation into some interesting virtues/abilities (like Puissant Faerie Lore, or initiating Faerie Magic, possibly even Free expression), and maybe you could allow that to happen outside of a Cult (depending how much you introduced your players to Mysteries and if you have or not access to HoH supplements).
So this PC is looking for clues for the next time the Knight wants to claim an orchard. He has understood enough that if he makes this story epic, grandiose, somehow, Faerie will reward him - not the Knight, but somehow the Realm of Faerie - his knowledge (NPCs or books) is a bit fuzzy on what/how it really happens, but he knows he is onto something.
So when the PCs confronts the Knight, he find out that he needs to make it looks like an heroic quest: once he is in the soon-to-be claimed orchard he makes a big show of swearing that he will "Defeat the evil that lurks in the roots of this land, claiming the work of an honest man and depriving him of what would feed his family. He will not let a honest man be drag into misery.".
Then he challenged the Knight to a duel, that he will loose (ideally, without dying himself - the Knight takes the challenge seriously, and although he is not a murderous maniac, is still a powerful foe as long as he has not been weaken). Then, once defeated, the PC swear to come get his revenge within a season, when the harvest is due. They might even agree on a wager set between the Knight and the PC - valuable item, promise of becoming the squire of the winner for a year and day, etc.
As the PC recovers, he might come a few times to the orchard, threatening the knight, remembering him of his promise to defeat him, even making an event of the next duel, inviting villagers or other sodales: giving an opportunity for the Knight to shine!
Then the second duel happens. The first few rounds seems to be in favour of the Knight until the PC pulls out his secret weapon (the vinegar) evening the fight - if the PC seems to have enough control, making looks like the combat is going back and forth until he manages to defeat "his valorous and beloved enemy" and winning the wager.
By allowing the Knight-Crab to have his fifteen minutes of fame, he is becoming more powerful (gaining vitality) and in return, the PC(s) are getting some form of boons, like the helmet of the knight, beside allowing to brew the potion to clear the curse contains vis, or the orchard will blooms twice a year, with an exceptional winter crop, for seven years.
Now, the faerie expert has validated his hypothesis and get understanding of the nature of faerie. Maybe he understands the final words of the Knight-Crab "Until we meet again...", gathering that the Knight-Crab could have become semi-cognizant and somehow knows that he can setup similar stories, but this time requiring different solutions, not claiming orchard, but possibly mines or fishing spots.
But he is also becoming more powerful, stakes becoming higher: what if instead of fishes or ore, he is starting to claim the sons or daughters of miners/fisherman. Finding his weakness becomes more difficult, more dangerous... etc.
At this stage, the PC understand the real nature of faeries, their needs, but also the danger they can represent, the benefit he can harness from them, but also that by making them more powerful by playing their game, by their rules, eventually he is creating more powerful and potentially dangerous threats for him or others. He can start looking at ways to short-cut stories weakening them, but also potentially alienating them (be careful of the Code and endangering the Order), he could also try to manipulate the story and change their role ("Ho thou, foul beast-knight that lurks into the ground, gnawing at the roots of three, foul serpent akin to the one who casted away Adam and Eve from the Garden, I will defeat you" - then suddenly, the Knight-Crab could become a dark faerie, snake-looking, more sinister, possibly poisonous - such attempt to change the nature of a faerie could be another challenge to discover more powers and keep progressing in initiation of Faerie Mysteries).
By staging this discovery both in-game for PCs and players, it will avoid to have a big info dump for the faerie expert (because he has 5 + Puissant in Faerie Lore) at early stage, and having to explaining him every time there is faerie of what he could do. Let the players "live" the understanding and discovery process.
Even if he has already 5 + Puissant during the first adventure, he will only allow him to find cure and weakness faster, but not understand the "behind-the-seen motivation" (after all, even most faeries are unaware of that).
When the second adventure ends, uses his high-level of expertise to suggest a theory (if the player does not formulate it himself). And possibly how he could leverage this knowledge by turning a simple story into an heroic one - if it would be proven true. Hints at greater rewards than simply vis.
Finally, at the third story, once the PC/player is enjoying is newly found power, hints at the consequences of making a more powerful faerie and the concept of cognizant/semi-cognizant faerie.