test: add Playwright E2E infrastructure with smoke test

Set up Playwright with Chromium, dev server auto-start, test helpers
for seeding bots and programmatic auth. Added smoke spec that verifies
homepage and leaderboard load without crashes.

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

package.json

@@ -10,9 +10,11 @@
     "lint": "eslint .",
     "typecheck": "vue-tsc --noEmit -p frontend/tsconfig.json && tsc --noEmit -p server/tsconfig.json",
     "clean": "rm -rf frontend/dist server/dist",
-    "seed": "pnpm --filter server seed"
+    "seed": "pnpm --filter server seed",
+    "test:e2e": "playwright test --config e2e/playwright.config.ts"
   },
   "devDependencies": {
+    "@playwright/test": "^1.58.2",
     "@typescript-eslint/eslint-plugin": "^8.56.1",
     "@typescript-eslint/parser": "^8.56.1",
     "concurrently": "^9.1.2",