Sure! I think I have a few real-world things I'd like to throw at you in terms of environment, and see how they vibe with you
I'm not insistent on any of these things, but I love nature and animals so I thought putting them out there might be helpful!
For one, a holiday/important season for them could be in late summer/early autumn with a wildberry season. In the US, there are
regions that have this with huckleberries (or I'm pretty sure it's huckleberries, I may be misremembering). Huckleberries grow wild and must be found, and is something a lot of folks in regions with this will partake in even though, obviously, the US has crops. That could just be a peaceful holiday idea to build off of.
In terms of flying fauna, it doesn't actually need to be too fantasy (if you don't want to) if they also don't commonly have visitors. Nature has had giant birds, some only recently going extinct (Haast Eagle). Giant birds in the recent past were either enormous scavenging vultures (ex, Teratorns), or, in the case of the Haast Eagle, big boy predators of even bigger non-flying birds called Moas.
The reason the Haast Eagle went extinct actually was due to forest destruction and over-hunting of the moa due to early settlers. Perhaps one of the reasons they are both not TOO hunting crazy and also isolationists is because they understand that whatever local wildlife they have, whatever you want it to be, is delicate and vulnerable like the moa. Something like that might feed well into the fact that they keep outsiders a bit at arm's length.
(I won't ramble about them but also if you want a big real-world lizard predator roaming about: Megalania)
With flying animals, be it griffons or wyverns or what have you, perhaps something they're particularly specialized in with mercenaries or just, in general, is defensive and offensive action against from-above attacks. Just a whole
culture that doesn't actually require the high ground to have an advantage. That doesn't have to always be in relation to military and warriors that way, since it's probably just good as an average joe to know what to do if a griffon shows up wanting to pluck you or your kid up.
If they're small-time crop growers, maybe they use every part of the
plant when possible. In example, if I grew tomatoes, I'd just make use of the tomatoes. But perhaps whatever crop these folks have they're able to turn a lot of the rest of the plant into fibers for weaving, or heck, making paper. There's a lot of different ways to make parchment, but woven papyrus is totally one of em! Making paper isn't easy in the given time period, and their method might be particularly fast and bountiful, making them important in trade routes.
(perhaps if there's a lot of griffons or birds around, then the less-delicious parts of the birds, or the eggshells, are ground into useful material, such as calcium supplements or fertilizer).
I don't know if you mean they'd maybe keep domesticated griffons, or if you just mean they'd be worshipped in that last post. In terms of folktales and stuff though, I think an interesting one is usually "how x got its x", and in this case it might be "how the griffon got its wings" or something, and perhaps the reason was to protect its young or something, and thus feed into the overall values of the culture.
If you wanna have domestic griffons unique to their culture I have a potential trade secret for them: egg care. So, the nature of eggs, even dinosaur eggs, is they can never be TOO big. This is because in order to support everything on the inside, the eggs need a level of thickness, but if an egg is too thick, then oxygen cannot permeate to the growing embryo inside (and for carbon monoxide to leave the same way). THEREFORE, perhaps something about domestic griffons is that there eggs ARE big, and the locals have a method of magic, or care, that ensures the eggs are "breathing". No one else outside the culture understands how they do this, and therefore cannot breed their own domestic griffons. A secret of their people.
This can lend into domestic griffons being bigger or growing faster than wild griffons, and probably having an innate love for people since they're cared for so hands-on since before they're even hatched. (Incidentally, an important part of domestication is the turn-around time to breed again; animals that take a long time to grow up aren't going to be domesticated as successfully.)
If you want to go crazy with domestication, you can get into specialty griffon breeding. We're talkin lean race griffins, striking war griffins, fluffy rescue griffins, big fat meat griffins, etc. Although something to keep in mind with livestock; during a famine, ideally, you want to be able to eat your livestock, and not have the livestock turn on you. This can be tackled in a few different ways, from undying loyalty, or just that these griffons are very unpicky eaters.
But anyways, if they have a method of making domestic griffon eggs breath, this might also mean that this element/school of magic is well learned and possibly expansive in their culture, lending itself into other parts of life outside of livestock. Air magic, helped breathing. It might mean they are able to care for their sick better if they practically have iron lung as a SPELL. The unique ability to help those rare ailments via this magic--and also a VERY deadly, yet inconspicuous, school of magic if used in mercenary work.