feat: Add automatic request handlers for app tool registration

Implement automatic `oncalltool` and `onlisttools` handlers that are
initialized when apps register tools. This removes the need for manual
handler setup and ensures tools work seamlessly out of the box.

- Add automatic `oncalltool` handler that routes calls to registered tools
- Add automatic `onlisttools` handler that returns full Tool objects with JSON schemas
- Convert Zod schemas to MCP-compliant JSON Schema using `zod-to-json-schema`
- Add 27 comprehensive tests covering automatic handlers and tool lifecycle
- Test coverage includes error handling, schema validation, and multi-app isolation

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

Author: ochafik

src/app-bridge.test.ts

@@ -1404,6 +1404,7 @@ describe("App <-> AppBridge integration", () => {
       });
     });
   });
+
   describe("AppBridge without MCP client (manual handlers)", () => {
     let app: App;
     let bridge: AppBridge;

src/app.ts

@@ -58,6 +58,7 @@ import {
   ToolCallback,
 } from "@modelcontextprotocol/sdk/server/mcp.js";
 import { ZodSchema } from "zod";
+import { zodToJsonSchema } from "zod-to-json-schema";
 
 export { PostMessageTransport } from "./message-transport";
 export * from "./types";
@@ -340,6 +341,27 @@ export class App extends Protocol<AppRequest, AppNotification, AppResult> {
       return;
     }
     this._toolHandlersInitialized = true;
+
+    this.oncalltool = async (params, extra) => {
+      const tool = this._registeredTools[params.name];
+      if (!tool) {
+        throw new Error(`Tool ${params.name} not found`);
+      }
+      return tool.callback(params.arguments as any, extra);
+    };
+    this.onlisttools = async () => {
+      const tools = Object.entries(this._registeredTools).map(
+        ([name, tool]) => ({
+          name,
+          description: tool.description,
+          inputSchema:
+            tool.inputSchema && "shape" in tool.inputSchema
+              ? zodToJsonSchema(tool.inputSchema as any)
+              : tool.inputSchema || { type: "object" as const, properties: {} },
+        }),
+      );
+      return { tools };
+    };
   }
 
   async sendToolListChanged(