Test extension upgrade compatibility (#10244)

## Problem
We have to test the extensions, shipped with Neon for compatibility
before the upgrade.
## Summary of changes
Added the test for compatibility with the upgraded extensions.

.github/workflows/build_and_test.yml

@@ -786,6 +786,17 @@ jobs:
           username: ${{ secrets.NEON_DOCKERHUB_USERNAME }}
           password: ${{ secrets.NEON_DOCKERHUB_PASSWORD }}
 
+      - name: Get the last compute release tag
+        id: get-last-compute-release-tag
+        env:
+          GH_TOKEN: ${{ secrets.CI_ACCESS_TOKEN }}
+        run: |
+          tag=$(gh api -q '[.[].tag_name | select(startswith("release-compute"))][0]'\
+            -H "Accept: application/vnd.github+json" \
+            -H "X-GitHub-Api-Version: 2022-11-28" \
+            "/repos/${{ github.repository }}/releases")
+          echo tag=${tag} >> ${GITHUB_OUTPUT}
+
       # `neondatabase/neon` contains multiple binaries, all of them use the same input for the version into the same version formatting library.
       # Pick pageserver as currently the only binary with extra "version" features printed in the string to verify.
       # Regular pageserver version string looks like
@@ -817,6 +828,20 @@ jobs:
           TEST_VERSION_ONLY: ${{ matrix.pg_version }}
         run: ./docker-compose/docker_compose_test.sh
 
+      - name: Print logs and clean up docker-compose test
+        if: always()
+        run: |
+          docker compose --profile test-extensions -f ./docker-compose/docker-compose.yml logs || true
+          docker compose --profile test-extensions -f ./docker-compose/docker-compose.yml down
+
+      - name: Test extension upgrade
+        timeout-minutes: 20
+        if: ${{ needs.tag.outputs.build-tag == github.run_id }}
+        env:
+          NEWTAG: ${{ needs.tag.outputs.build-tag }}
+          OLDTAG: ${{ steps.get-last-compute-release-tag.outputs.tag }}
+        run: ./docker-compose/test_extensions_upgrade.sh
+
       - name: Print logs and clean up
         if: always()
         run: |