Add Playwright E2E test suite (25 tests across 4 specs)

- playwright.config.ts: headless CI setup with JSON/HTML reporters
- e2e/global-setup.ts: app reachability check before tests
- e2e/auth.spec.ts: 6 auth tests (sign-in, session, protected routes)
- e2e/compare.spec.ts: 8 API tests (validation, SSE flow, DB persistence)
- e2e/comparisons.spec.ts: 6 CRUD tests (list, detail, 404, view counts)
- e2e/user.spec.ts: 5 user tests (stats, pagination, session binding)
- e2e/helpers.ts: shared SSE parsing, auth, URL resolution utilities
- e2e/README.md: setup and run instructions
- AGENTS.md: updated with LLM provider notes and testing docs
- .gitignore: added playwright report/result directories
- package.json: added @playwright/test and test:e2e scripts

package.json

@@ -6,7 +6,12 @@
     "dev": "next dev",
     "build": "next build",
     "start": "next start",
-    "lint": "eslint"
+    "lint": "eslint",
+    "test:e2e": "playwright test",
+    "test:e2e:ui": "playwright test --ui",
+    "test:e2e:headed": "playwright test --headed",
+    "test:e2e:report": "playwright show-report",
+    "test:e2e:install": "playwright install chromium"
   },
   "dependencies": {
     "@base-ui/react": "^1.4.1",
@@ -27,6 +32,7 @@
     "tw-animate-css": "^1.4.0"
   },
   "devDependencies": {
+    "@playwright/test": "^1.52.0",
     "@tailwindcss/postcss": "^4",
     "@types/node": "^20",
     "@types/react": "^19",