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>

Dockerfile

@@ -118,6 +118,12 @@ RUN curl -fsSL https://opencode.ai/install | bash && \
     echo "=== Checking OpenCode CLI installation ===" && \
     ls -la /home/automaker/.local/bin/ && \
     (which opencode && opencode --version) || echo "opencode installed (may need auth setup)"
+
+# Install Playwright Chromium browser for AI agent verification tests
+# This adds ~300MB to the image but enables automated testing mode out of the box
+RUN npx playwright install chromium && \
+    echo "=== Playwright Chromium installed ===" && \
+    ls -la /home/automaker/.cache/ms-playwright/ || echo "Playwright browsers installed"
 USER root
 
 # Add PATH to profile so it's available in all interactive shells (for login shells)