I'd love if those additional checks, not only on GitHub but in general, asked you to re-login via the regular login form so that it could be auto-filled by the browser (or other passwords managers) with the same reliability as the the regular login form is.

Now, it requires you to fish out and paste the password from the manager into this, yet another, special field.

EDIT: I know that some managers can guess when to use the password in a different context on the same site. But not all of them and not all the time.

Mozilla's manager (built into Firefox) doesn't do it properly on Google accounts page, or on GitHub. At least it didn't yesterday.