Cleanup: extract constants, fix typecheck, add ESLint, organize store types

- Remove unused initCount state from useAuthGate hook
- Replace magic number with MAX_SAVES_PER_USER constant in saves route
- Extract duplicated EMAIL_REGEX and MIN_PASSWORD_LENGTH in auth routes
- Fix game-simulation typecheck failure by adding DOM lib to tsconfig
- Extract store UI types (ActivePage, InfraNav, etc.) to store/types.ts
- Fix let→const for non-reassigned arrays in servingPipeline
- Fix useless initial assignments in reputationSystem
- Fix ambiguous multiline array access in sanityChecks
- Add minimal ESLint config with typescript-eslint
- Add .planning/ and *.log to .gitignore

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

package.json

@@ -5,7 +5,7 @@
     "dev": "turbo dev",
     "build": "turbo build",
     "typecheck": "turbo typecheck",
-    "lint": "turbo lint",
+    "lint": "eslint .",
     "test": "vitest run",
     "test:watch": "vitest",
     "clean": "turbo clean",
@@ -13,8 +13,11 @@
     "simulate:ci": "pnpm --filter @token-empire/game-simulation simulate:ci"
   },
   "devDependencies": {
+    "@eslint/js": "^10.0.1",
+    "eslint": "^10.2.1",
     "turbo": "^2.5.0",
     "typescript": "^5.8.0",
+    "typescript-eslint": "^8.59.1",
     "vitest": "^4.1.5"
   },
   "packageManager": "pnpm@10.33.0",