Hi Sasha;
I wonder if you ever received the results of your nasal microbiome?
I seem to have a disturbance in the sinuses that occurs along with the gut. I think it's an overgrowth, (bacterial), but I've not had it tested.
Both my sinuses and gut respond to dietary and anti-microbial treatments. I see it's such an individual thing, but, I'll just write about what's been helping the most. Following Chris Kresser's advice has helped, especially concerning SIBO. Lowering high FODMAP foods has been one of the most helpful.
Diet alone hasn't been enough, so I've tried some antimicrobial herbs, mostly essential oils. Thyme essential oil, taken internally, has been the best, so far. Thyme Oil is controversial, many people discourage its use internally, but it appears to be no more toxic than most other essential oils. ( I add 5-7 drops to an empty capsule, then dilute with olive oil.) I usually take it with meals, but sometimes alone. The only side effect I've had was some burps.
Another treatment I've used, which is very strong, and should come with a caution, is hydrogen peroxide, 3 %. I put it in an empty nasal spray bottle, and shoot once into each nostril. It burns and foams. I hold my nose and add pressure by trying to breathe out for a few seconds. Then I blow my nose to expel the peroxide, etc.
I realize that this method would be too extreme for many to try, ( and painful ), but it's about the only way that's worked for me.
It's possible that the green tea helps, because it is a folate antagonist. This is an odd guess, but from my experience, when I have high folate foods, supplements, or even highly fermentable foods, I'll get sinus inflammation. ( with headaches then migraines)
Folate can be produced from gut bacteria, which can be good, but in excess,it can be inflammatory.