refactor: eliminate code duplication (DRY principle) (#211)

## Problem Solved
Previous refactoring added 105 lines (1476→1581) by extracting code into separate files without eliminating duplication. This refactor focuses on reducing code size through deduplication while maintaining file separation for maintainability.

## Summary
- Reduced total lines from 1581 to 1519 (-62 lines, 3.9% reduction)
- Eliminated duplicate patterns using generic helpers and factory functions
- Maintained file structure for maintainability
- Zero functional changes - same behavior

### Phase 1: DRY use-quota-manager.tsx
- Created parseStorageCount() helper (eliminates 6x localStorage read duplication)
- Created createQuotaChecker() factory (consolidates 3 check function bodies)
- Created createQuotaIncrementer() factory (consolidates 3 increment function bodies)
- Result: 242→247 lines (+5 lines, but fully DRY with eliminated duplication)

### Phase 2: DRY chat-panel.tsx (1176→1109 lines, -67 lines)

#### 2.1: Extract checkAllQuotaLimits helper
- Replaced 3 occurrences of 18-line quota check blocks
- Saved 36 lines

#### 2.2: Extract sendChatMessage helper
- Replaced 3 occurrences of 21-line sendMessage+headers blocks
- Saved 42 lines

#### 2.3: Extract processFilesAndAppendContent helper
- Replaced 2 occurrences of file processing loops
- Handles PDF, text, and image files uniformly
- Async helper with optional image parts parameter

lib/storage.ts

@@ -0,0 +1,27 @@
+// Centralized localStorage keys
+// Consolidates all storage keys from chat-panel.tsx and settings-dialog.tsx
+
+export const STORAGE_KEYS = {
+    // Chat data
+    messages: "next-ai-draw-io-messages",
+    xmlSnapshots: "next-ai-draw-io-xml-snapshots",
+    diagramXml: "next-ai-draw-io-diagram-xml",
+    sessionId: "next-ai-draw-io-session-id",
+
+    // Quota tracking
+    requestCount: "next-ai-draw-io-request-count",
+    requestDate: "next-ai-draw-io-request-date",
+    tokenCount: "next-ai-draw-io-token-count",
+    tokenDate: "next-ai-draw-io-token-date",
+    tpmCount: "next-ai-draw-io-tpm-count",
+    tpmMinute: "next-ai-draw-io-tpm-minute",
+
+    // Settings
+    accessCode: "next-ai-draw-io-access-code",
+    closeProtection: "next-ai-draw-io-close-protection",
+    accessCodeRequired: "next-ai-draw-io-access-code-required",
+    aiProvider: "next-ai-draw-io-ai-provider",
+    aiBaseUrl: "next-ai-draw-io-ai-base-url",
+    aiApiKey: "next-ai-draw-io-ai-api-key",
+    aiModel: "next-ai-draw-io-ai-model",
+} as const