Admin Bar should consistently use the user locale on both frontend and backend

[ixiter]

The Admin Bar uses a different locale depending on whether it is displayed in the admin backend or on the site frontend.

In the admin backend, it uses the user's selected language. On the site frontend, it uses the site's language.

Since the Admin Bar is a user-specific interface element, it should consistently use the user's selected language in both contexts.

This becomes confusing when the Admin Bar appears in German in the admin backend, but in English on the site frontend for the same logged-in user.

[sabernhardt]

This is tracked on #38643.