As long as they don't scan the card (I've never seen a bank do that) and the photo matches your face and the information matches what's in your paperwork you should be totally fine.
If you have cash you can deposit it into your account but will need the account number or bank card associated to it. Your expired Photo ID can still be used to verify who you are.
If it expires today, then it is good until midnight tonight.
You also shouldn't need an ID for a deposit in the first place.
No ID required to deposit cash.
Why would your bank make you show ID to deposit cash?
Your ID is not expired until midnight tonight. So if you go to the bank today, your ID is current and should be acceptable
