It's been long I registered on binance, I noticed no much verification, but there were. I could have been forgetting, but I think phone number was required at the time.

For p2p  trading, there will be additional verification, in a way you will be asked to snap your real face. Making use of credit card to purchase, that is another KYC as you are linked to your bank account.

I think going for completely decentralized exchanges will be good rather than centralized exchanges which people may think they require no KYC while having different tactics to make customer to verify their account, Bsiq has a very good tradig volume which makes it the number decentralized exchange in my opinion.