fix: missing "properties" property in empty schema

src/server/mcp.test.ts

@@ -265,6 +265,7 @@ describe("tool()", () => {
     expect(result.tools[0].name).toBe("test");
     expect(result.tools[0].inputSchema).toEqual({
       type: "object",
+      properties: {},
     });
 
     // Adding the tool before the connection was established means no notification was sent

src/server/mcp.ts

@@ -1018,6 +1018,7 @@ export type RegisteredTool = {
 
 const EMPTY_OBJECT_JSON_SCHEMA = {
   type: "object" as const,
+  properties: {},
 };
 
 // Helper to check if an object is a Zod schema (ZodRawShape)