Summary

• Add an unread-message badge to the top Mail menu item using the existing folder count stream.
• Hide the badge when the unread total is zero and keep the Mail link's accessible label in sync with the count.
• Add focused coverage for the header toolbar badge rendering.

Closes #784

Tests

• npm ci
• npx ng test --watch=false --browsers=FirefoxHeadless --include=src/app/menu/headertoolbar.component.spec.ts
  • test-only commit failed before the implementation with TOTAL: 1 FAILED, 0 SUCCESS
  • implementation passed with TOTAL: 1 SUCCESS
• npx tsc -p src/tsconfig.app.json --noEmit
• npx tsc -p src/tsconfig.spec.json --noEmit
• npm run lint -- --quiet
• npm run policy
• git diff --check origin/master...HEAD
• git show --check --stat --oneline HEAD
• PowerShell-native production build sequence:
  • $env:SKIP_CHANGELOG='1'; node src/build/pre-build.js; npx ng build --configuration production --base-href=/app/ runbox7; node src/build/post-build.js
  • passed with existing Angular/CommonJS/theming warnings; build hash 254ae4785eb28f9b

AI disclosure

I used OpenAI Codex (GPT-5) in my local development environment to inspect the issue and current source, implement the code and focused test, and run the validation commands listed above.