Earlier quoted context omitted.
The second factor isn’t a second device, it’s the TOTP code.
No, factors are supposed to have different qualities, such as: "Something you know"; "something you have"; "something you do"; "something you are [biometrics]"; "somewhere you are [geolocation]". Passwords are in your head - "something you know". TOTP codes are generated by a hardware token - "something you have". If the TOTP codes are crammed into your password manager, then the factors are no longer distinguished b…
Logging in through a password manager requires that you know a password (your master password), and have a file (your vault).