Fix language model selector (#26138)

This PR fixes the language model selector.

I tried to piece together the state prior to #25697 (the state it was in
at 11838cf89e0b96531f90f22432b3df6859587871) while retaining unrelated
changes that happened since then.

Release Notes:

- Fixed an issue where language models would not be authenticated until
after the model selector was opened (Preview only).