test: add Playwright E2E test suite (30 tests)

Add browser-level end-to-end tests covering public pages, Keycloak
OAuth authentication flow, dashboard interactions, providers config,
developer section, organization pages, and sidebar navigation.

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

.gitignore

@@ -22,3 +22,8 @@ keycloak/*
 node_modules/
 
 searxng/
+
+# Playwright
+e2e/.auth/
+playwright-report/
+test-results/