refactor: improve AI event handling and conflict display in chat

- AI fetches events on-demand via callbacks for better efficiency
- Add conflict detection with warning display when proposing overlapping events
- Improve event search and display in chat interface
- Load full chat history for display while limiting AI context

apps/server/src/app.ts

@@ -96,8 +96,10 @@ app.post("/api/ai/test", async (req, res) => {
     const result = await aiProvider.processMessage(message, {
       userId: "test-user",
       conversationHistory: [],
-      existingEvents: [],
       currentDate: new Date(),
+      fetchEventsInRange: async () => [],
+      searchEvents: async () => [],
+      fetchEventById: async () => null,
     });
     res.json(result);
   } catch (error) {