TOTP tokens on my wrist with the smartest dumb watch

I used totp first time yesterday on GitHub and I don't understand it's point. I had to install otpclient app (from Ubuntu repository) where I typed 4 strings and it spit out one number which I typed back to GitHub. Attacker could do this as well, so the only thing totp does is to prove I can read and write. What am I missing here?

It's supposed to be on another independent device.

Doesn't have to be. While storing them on your computer does not protect you from an adversary with access to your computer, it still protects you against an advrsaey e that intercepts (or guesses, maybe after a breach) your password.

It doesnt have to be yes, but it's called 2 factor auth because of the reason that your computer is 1 factor and another device is 2.

It won't protect you from the intention 2fa was created.

The second factor isn't about a second device. It is additional to something you know (password), typically the second factor is something you have (device, yubikey, etc.).

The idea being that the intersection of {people who can get your password, such as through phishing or other digital attack} and {people who have physical proximity and can steal your physical device} are typically much smaller than the set of people in either category.