Start GitHub linking: either full App install or OAuth-only (user-to-server). ``**_kwargs`` absorbs ``parent_lookup_uuid`` from the nested ``/api/users/{uuid}/integrations/`` router (same pattern as ``local_evaluation`` under projects). Usually returns ``install_url`` pointing at ``/installations/new`` so the user can pick any GitHub org (new or already connected). GitHub's install page handles both cases: orgs where the app is installed show "Configure" (no admin needed), orgs where it isn't show "Install" (needs admin). **OAuth fast path:** when the current project already has a team-level GitHub installation, and the user has no ``UserIntegration`` for that installation yet, we skip the org picker and redirect straight to ``/login/oauth/authorize`` so the user only authorizes themselves. ``connect_from`` is preserved for first-party clients so they return to the originating client immediately. In both cases the response key is ``install_url`` for compatibility with callers.