@OP I don't think it would ask for a password because mine only asks for a 2FA code when withdrawing after entering the 2FA it will ask if you gonna approve the transaction or not and then the 2nd email will receive a link to approve the transaction.
Are you saying you have fund in coinbase multi-sig vault and you are able to withdraw fund from that just with entering the 2FA code and email verification? How is that possible? As already, they no longer supports multi-sig vault.
I feel you are confusing coinbase mutli-signature wallet with their custodial wallet.