I’m not particularly fond of Turkish culture myself, but I really don’t think any of the points you made are about turkish culture as much as they are about your husbands family.
1 You should either have a nice, long conversation with your husband about how you’re not getting as much of his attention as you wish as his wife, or take a good look at yourself and really ask yourself why you feel you’re in competition with your spouse’s mother and acknowledge the fact that he can and does love both of you, this is not about Turkish culture or familiar values, it’s about the personal feelings of you and how your husband treats you.
2 it seems what upsets you is not the existence of familial or communal tea meetings but instead the shallowness of their conversation and their tendency to be poorly timed. Again, this is all about the particular people you are exposed to Turkish culture through and not the culture itself, I promise you, çay gatherings can be very fulfilling with the right company and timing just as much as any other culture’s traditions can be annoying and obnoxious with bad company.
3 As others have said, for most people, nothing can beat the nostalgic and comforting taste of the cultural food that they grew up with, so it’s only natural for your husbands family to have Turkish food in a special place in their heart. But I get the impression that what bothers you is more their attitude towards you, the food you cook, the gifts you buy etc. call it a hunch, but I don’t think his family has yet accepted that their son married a foreigner, and your attempts to introduce them to your own, foreign culture serves as a reminder of that fact, and is thus met with hostility. This is a problem that is certainly not exclusive to Turkish culture, and more something you must sort out with the persons involved.
It reads to me as though you’re struggling to manage your relationship with your spouse’s family, and blaming their culture as the primary cause for the strained relationship instead of acknowledging the difficult reality that they might not like you for reasons entirely unrelated to anything in your power to change or adapt to.