Chat sign-in: auto-enable GitHub Authentication extension if silently disabled (#296303)

* Initial plan

* Auto-enable GitHub Authentication extension during chat sign-in if disabled

Co-authored-by: TylerLeonhardt <[email protected]>

* Apply during the chat request

* feedback

* delete the tests that didn't exist in the first place

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Co-authored-by: copilot-swe-agent[bot] <[email protected]>
Co-authored-by: TylerLeonhardt <[email protected]>
Co-authored-by: Tyler Leonhardt <[email protected]>