TOTP is not as secure as WebAuthn, because if you enter the TOTP code into a phishing site, the phisher can now successfully authenticate as you. WebAuthn was specifically designed to be immune to this case: if you were to use your WebAuthn key in a phishing website, the phisher would not then be able to authenticate as you on the real site.

You have to have the generator somewhere to get the code. If it's in software, you must have access to that software, and it must be secure. With WebAuthN, it can be a hardware token and usually multiple of them stored in various locations that only you can access (safe deposit box, physical safe, etc).