Does ECDSA.sol work on Binance Smart Chain?

if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }
        if (v != 27 && v != 28) {
            return (address(0), RecoverError.InvalidSignatureV);
        }

Can someone explain how the compatibility work or point out to some source?

OZ's ECDSA.sol works the same on BSC as on ETH.

Yes, ECDSA signatures are valid independent of the chain.