Backups not showing in my list

You have two good responses to your issue above. I would add one more thing to the resolution and that is, the backup was made on a newer iOS version than the phone you’re restoring to.

Ensure that the backup was created with the same or older iOS version than the iOS version that is on the iPhone to be restored.

Axel F.

You have either logged in to the iPhone using a different Apple ID or have not backed up this device on the Apple ID that it is currently logged into.

When was the last time you backed up? Did you back up to iCloud or a computer?