I use bitwarden to store my 2fa codes. If you run vaultwarden yourself, you only need the client app to access it.
Discussion
You need their Pro version for 2fa (or run your own instance) right? The guy this would be for probably wouldn't want to do either. I'm just trying to find one that doesn't do account backups and let's you keep track of your keys inside the app while preferably being a well used open source project. These might be high standards lol