Unfortunately you will not get your coins back without sacrificing your privacy.

Centralized exchanges pull this crap all the time. Binance are particularly bad for it, but they certainly aren't the only exchange which does this. Advertise a no-KYC account, let users open an account without KYC, let users deposit coins without KYC, let users trade and pay fees without KYC, but as soon as you want to withdraw, suddenly your account is flagged for unspecified and undefined "suspicious activity". Your account is frozen, and you have to decide whether your give up your documents or give up your coins.

They never tell you why your account was flagged, and they also don't let new users what things not to do to avoid having their account flagged. Anything from logging in from a different IP (which is ridiculous since IPs change all the time, and you will have different IPs on different devices) to depositing or withdrawing from "suspicious" addresses (again, without them telling you what criteria they use to classify addresses) will result in your account being locked. Binance's advertised "2 BTC Unverified Account" seems to be a blatant lie at this point.