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>

packages/game-engine/src/systems/market/servingPipeline.ts

@@ -75,7 +75,7 @@ interface CachedSlot {
 }
 
 let cachedDeploymentVersion = -1;
-let cachedSlots: CachedSlot[] = [];
+const cachedSlots: CachedSlot[] = [];
 const fleetOutput: ModelServingSlot[] = [];
 
 const mainRemaining = new Map<string, number>();
@@ -83,7 +83,7 @@ const mainUsed = new Map<string, number>();
 const entRemaining = new Map<string, number>();
 const entUsed = new Map<string, number>();
 
-let cachedUtilization: ModelUtilizationEntry[] = [];
+const cachedUtilization: ModelUtilizationEntry[] = [];
 
 export function resetFleetCache(): void {
   cachedDeploymentVersion = -1;