Auth with passwords + Playwright E2E tests + PostHog analytics

- bcrypt password hashing in auth (register, login, change-password)
- Login/register pages with password fields
- Profile update + OAuth placeholder endpoints
- Playwright test suite: auth, pages, API (3 test files)
- PostHog Docker analytics on :8010

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

.gitignore

@@ -3,3 +3,5 @@ node_modules/
 .env
 *.log
 .claude/
+test-results/
+test-results.json