docs: inject version selector to HTML docs (#2886)

* docs: inject version selector to HTML docs

* Apply suggestions from code review

.github/workflows/docs-build.yml

@@ -98,12 +98,26 @@ jobs:
         uses: google-github-actions/auth@v2
         with:
           credentials_json: ${{ secrets.GCS_SA_KEY }}
-
       - name: Setup gcloud
         uses: google-github-actions/setup-gcloud@v2
         with:
           project_id: ${{ secrets.GCS_PROJECT }}
 
+      # Uploading docs as archive to GCS, so they can be as backup
+      - name: Upload docs as archive to GCS 🪣
+        if: startsWith(github.ref, 'refs/tags/')
+        working-directory: docs/build
+        run: |
+          zip ${{ github.ref_name }}.zip -r html/
+          gsutil cp ${{ github.ref_name }}.zip ${GCP_TARGET}
+
+      - name: Inject version selector
+        working-directory: docs/build
+        run: |
+          pip install -q wget
+          python -m wget https://raw.githubusercontent.com/Lightning-AI/utilities/main/scripts/inject-selector-script.py
+          python inject-selector-script.py html torchmetrics
+
       # Uploading docs to GCS, so they can be served on lightning.ai
       - name: Upload docs/metrics/stable to GCS 🪣
         if: startsWith(github.ref, 'refs/heads/release/')
@@ -118,11 +132,3 @@ jobs:
       - name: Upload docs/metrics/release to GCS 🪣
         if: startsWith(github.ref, 'refs/tags/')
         run: gsutil -m rsync -d -R docs/build/html/ ${GCP_TARGET}/${{ github.ref_name }}
-
-      # Uploading docs as archive to GCS, so they can be as backup
-      - name: Upload docs as archive to GCS 🪣
-        if: startsWith(github.ref, 'refs/tags/')
-        working-directory: docs/build
-        run: |
-          zip ${{ github.ref_name }}.zip -r html/
-          gsutil cp ${{ github.ref_name }}.zip ${GCP_TARGET}