> competent attackers will simply run their code from the victim's browser and session
What do you mean? JS even on the same page can't read HTTPOnly cookies. If you are assuming that the browser has been hacked then it is pretty much game over regardless of what you use.
We are talking about XSS, where an attacker can run their JS code on your page. If the attacker can run JS on your page, they can already do whatever your signed-in user can do. No need to read the cookie to make authenticated requests, just like your own code doesn’t need to read the cookie.
What do you mean? JS even on the same page can't read HTTPOnly cookies. If you are assuming that the browser has been hacked then it is pretty much game over regardless of what you use.