I have my backup codes in a file that's encrypted using a key derived from a passphrase that's over 50 characters long (not the same passphrase used for my password manager), that I've memorized. It's stored in cloud storage, on an account created just for that purpose. The account is protected with a (different) password that I've also memorized, and that account doesn't have any kind of MFA on it.
Since access only requires 1) internet access, 2) a common, publicly-available decryption program, and 3) stuff in my brain, I can gain access to it under pretty much any situation where I'd need access to it.
A potential downside is that if I ever had to access and decrypt the file on hardware I don't trust, I'd have to revoke and re-issue all my backup codes, and come up with a new long passphrase to protect the new file, which is a huge pain to do.
This is of course not perfect security, but I think it's fine for my purposes and threat model.