fix(docker): Pre-install Playwright Chromium browsers for automated testing

Fixes #725

AI agents in automated testing mode require Playwright to verify implementations,
but Docker containers had only system dependencies installed, not browser binaries.
This caused verification failures with permissions errors.

Changes:
- Install Playwright Chromium in Dockerfile (~300MB increase)
- Update docker-compose.override.yml.example with clearer Playwright documentation
- Add "Playwright for Automated Testing" section to README
- Document optional volume mount for persisting browsers across rebuilds

Browsers are now pre-installed and work out of the box for Docker users.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

docker-compose.override.yml.example

@@ -21,9 +21,13 @@ services:
       # - ~/.local/share/opencode:/home/automaker/.local/share/opencode
       # - ~/.config/opencode:/home/automaker/.config/opencode
 
-      # Playwright browser cache - persists installed browsers across container restarts
-      # Run 'npx playwright install --with-deps chromium' once, and it will persist
+      # ===== Playwright Browser Cache (Optional) =====
+      # Playwright Chromium is PRE-INSTALLED in the Docker image for automated testing.
+      # Uncomment below to persist browser cache across container rebuilds (saves ~300MB download):
       # - playwright-cache:/home/automaker/.cache/ms-playwright
+      #
+      # To update Playwright browsers manually:
+      #   docker exec automaker-server npx playwright install chromium
     environment:
       # Set root directory for all projects and file operations
       # Users can only create/open projects within this directory
@@ -37,6 +41,7 @@ services:
       # - CURSOR_API_KEY=${CURSOR_API_KEY:-}
 
 volumes:
-  # Playwright cache volume (persists Chromium installs)
+  # Playwright cache volume - optional, persists browser updates across container rebuilds
+  # Uncomment if you mounted the playwright-cache volume above
   # playwright-cache:
   #   name: automaker-playwright-cache