ci: remove migration push from search action (#28327)

We don't need this for migration pushes since the Supabase integration will do
it instead. Removing it makes this action less brittle since embedding updates
get blocked on CLI problems.

.github/workflows/search.yml

@@ -23,11 +23,8 @@ jobs:
 
     env:
       OPENAI_API_KEY: ${{ secrets.OPENAI_API_KEY }}
-      SUPABASE_ACCESS_TOKEN: ${{ secrets.SUPABASE_ACCESS_TOKEN }}
-      PROJECT_ID: ${{ secrets.SEARCH_SUPABASE_PROJECT_ID }}
       NEXT_PUBLIC_SUPABASE_URL: ${{ secrets.SEARCH_SUPABASE_URL }}
       SUPABASE_SERVICE_ROLE_KEY: ${{ secrets.SEARCH_SUPABASE_SERVICE_ROLE_KEY }}
-      SUPABASE_DB_PASSWORD: ${{ secrets.SEARCH_SUPABASE_DB_PASSWORD }}
       SEARCH_GITHUB_APP_ID: ${{ secrets.SEARCH_GITHUB_APP_ID }}
       SEARCH_GITHUB_APP_INSTALLATION_ID: ${{ secrets.SEARCH_GITHUB_APP_INSTALLATION_ID }}
       SEARCH_GITHUB_APP_PRIVATE_KEY: ${{ secrets.SEARCH_GITHUB_APP_PRIVATE_KEY }}
@@ -49,12 +46,6 @@ jobs:
       - name: Download dependencies
         run: npm ci
 
-      - name: Link Supabase project
-        run: npx supabase link --project-ref $PROJECT_ID
-
-      - name: Run migrations
-        run: npx supabase db push
-
       # Need the miscellaneous use API, which is available publicly (by design) in www
       - name: Copy environment variables
         run: cp apps/www/.env.local.example apps/docs/.env