Well, I'm not a user of BingX, and I also don't know whether they have a certain threshold allowed for non-verified users, but their customer agreement is self-explanatory. It's clear and straightforward. And it doesn't say that personal information may be requested and shared if you use their P2P services. Rather, it says that "by creating an account on BingX", you agree that your personal information may be requested and shared. That's unequivocal.
I cross-checked and non-verified accounts are indeed welcome, see:
https://bingx.com/en-us/support/articles/4576854622361-BingXTutorialHowtoCompleteKYCorIdentityVerification/But in such cases, I like the term no-mandatory kyc more instead of a flat no-kyc. Though OP most likely is accepting the former as well since kucoin is mentioned which was a no-mandatory kyc exchange previously.