How do bitcoin bridges work?

I understand how bridges work from protocols with a code execution environment, ethereum solana, cosmos ect.. to other protocols with a code execution environment work. My question is how does the bridge on the Bitcoin side work? What structure is used to hold the coins in reserve? Where does the users proof of ownership of the tokens get sent and verified, and how? Since Bitcoin as far as I am aware is Turing incomplete and doesn’t store byte code for later exe like the evm shouldn’t it be impossible to generate and verify proofs on chain?