Use any password manager (you should already be using one) that has TOTP support such as keepassxc or 1Password. No cellphone needed.
[1] https://www.nongnu.org/oath-toolkit/oathtool.1.html [2] https://datatracker.ietf.org/doc/html/rfc6238
This applies to logging in to the GitHub Web application.
Laptop or phone stolen? No access to your own devices? Oops guess you can't login to anything.
Having a unique password per service solves that particular issue. But you're right that there's a "price" in that losing access to your passwords would leave you screwed. I'd strongly recommend making sure you at least memorize your email password, as well as backing it up in several places.
The scenarios in which you are unable to use your password manager are far more likely than you're making it seem.