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>

package.json

@@ -4,6 +4,7 @@
   "type": "module",
   "private": true,
   "devDependencies": {
+    "@playwright/test": "^1.52.0",
     "@types/bun": "latest"
   },
   "peerDependencies": {