Add the browser tests in Docker Compose to CI jobs

Author: sbp

.github/workflows/build.yml

@@ -43,7 +43,10 @@ jobs:
         #if: steps.cache.outputs.cache-hit != 'true'
         run: uv sync --no-dev --group test
 
-      # Run tests
-      - name: Run tests
+      - name: Run unit tests
         run: |
           uv run --no-sync pytest -rs tests
+
+      - name: Run Playwright end-to-end tests
+        run: |
+          sh tests/run-tests.sh