fix: add completions capability for Cursor compatibility (#209)

* fix: add completions capability for Cursor compatibility

Add completions capability and return empty completions for unsupported
types instead of throwing errors. This fixes Cursor startup failures
when MCP servers require the completions capability.

Related to: eyaltoledano/claude-task-master#1413

* style: fix prettier formatting

* add tests to prevent regression of cursor completions issue

* fix: advertise completions capability for Cursor compatibility

Add completions capability to server capabilities to prevent Cursor
from failing to start when the capability is not advertised.

Author: Justiceleeg

src/FastMCP.test.ts

@@ -1812,6 +1812,45 @@ test("completes template resource arguments", async () => {
   });
 });
 
+test("advertises completions capability to prevent Cursor startup error", async () => {
+  await runWithTestServer({
+    run: async ({ client }) => {
+      // The server should advertise completions capability, allowing Cursor to start
+      // Verify that completion requests are handled (capability is advertised)
+      // by attempting a completion request - it should not throw "method not found"
+      try {
+        await client.complete({
+          argument: {
+            name: "test",
+            value: "value",
+          },
+          ref: {
+            name: "nonexistent-prompt",
+            type: "ref/prompt",
+          },
+        });
+      } catch (error) {
+        // It's okay if it throws an error about unknown prompt
+        // The important thing is it doesn't throw "method not found"
+        // which would indicate the capability isn't advertised
+        if (error instanceof McpError) {
+          expect(error.code).not.toBe(ErrorCode.MethodNotFound);
+        }
+        // If it's not an McpError (e.g., UnexpectedStateError), that's fine too
+        // It means the method exists and the capability is advertised
+      }
+    },
+    server: async () => {
+      const server = new FastMCP({
+        name: "Test",
+        version: "1.0.0",
+      });
+
+      return server;
+    },
+  });
+});
+
 test("lists resource templates", async () => {
   await runWithTestServer({
     run: async ({ client }) => {

src/FastMCP.ts

@@ -1048,6 +1048,8 @@ export class FastMCPSession<
 
     this.#capabilities.logging = {};
 
+    this.#capabilities.completions = {};
+
     this.#server = new Server(
       { name: name, version: version },
       { capabilities: this.#capabilities, instructions: instructions },