>Now, my Github access depends on the second factor, which I have chosen to be Microsoft Authenticator running on my phone. I genuinely do not know what will happen if my phone breaks down, so I downloaded TOTP codes from Github and even tried one to see if it works, and so far it does, but now I have one less TOTP code to use in case something happens. Moreover, since Github is now a special case for my password management routine, I am afraid I may loose those TOTP codes and be totally locked out of my account.
You don't need a phone for this. You can put the secret key into your password manager and it can generate the TOTP code whenever you need it. KeepassXC and 1Password support it.
It stretches the definition of "two-factor" but I don't care; like the author I'm more concerned about phone theft and losing access to everything.