feat: replace Claude with GPT for AI chat integration

- Replace ClaudeAdapter with GPTAdapter using OpenAI GPT (gpt-5-mini)
- Implement function calling for calendar operations (getDay, proposeCreate/Update/Delete, searchEvents)
- Add provider-agnostic AI utilities in ai/utils/ (systemPrompt, toolDefinitions, toolExecutor, eventFormatter)
- Add USE_TEST_RESPONSES env var to toggle between real AI and test responses
- Switch ChatService.processMessage to use real AI provider
- Add npm run format command for Prettier
- Update CLAUDE.md with new architecture

apps/server/src/ai/utils/index.ts

@@ -0,0 +1,13 @@
+export {
+  formatExistingEvents,
+  formatDate,
+  formatTime,
+  formatDateTime,
+} from "./eventFormatter";
+export { buildSystemPrompt } from "./systemPrompt";
+export {
+  TOOL_DEFINITIONS,
+  type ToolDefinition,
+  type ParameterDef,
+} from "./toolDefinitions";
+export { executeToolCall, type ToolResult } from "./toolExecutor";