Do you save 2FA “backup codes”?

I'm going to guess you just got one from Docker Hub today, because I did too. I saved the code, alongside the password in my password manager, which itself already requires 2FA to open. Still, seems like it defeats some of the point of the security to store it in the same place as the password...

I save mine here: https://www.arcanus55.com/?trusted55=A55PV2

Yes. I store them offline, in keepass or screenshots.

Which app are you using?

Google Authenticator for Android, eg, will let you generate a QR code. Others can back up to the cloud.