feat: add Playwright E2E and API regression test suite

Production-ready test infrastructure with Page Object Model pattern,
reusable fixtures for auth/DB/test-data, and example tests covering
login flow, dashboard, accounts CRUD API, and visual regression.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

.gitignore

@@ -44,3 +44,13 @@ coverage/
 
 # TypeScript
 *.tsbuildinfo
+
+# Playwright
+/test-results/
+/playwright-report/
+/blob-report/
+tests/.auth/
+*-snapshots/
+
+# Test environment
+.env.test