Fix async resource functions not being awaited (#1092)

Co-authored-by: Marcelo Trylesinski <marcelotryle@gmail.com>

tests/issues/test_188_concurrency.py

@@ -1,12 +1,13 @@
 import anyio
 import pytest
+from pydantic import AnyUrl
 
 from mcp.server.fastmcp import FastMCP
 from mcp.shared.memory import create_connected_server_and_client_session as create_session
 
 
 @pytest.mark.anyio
-async def test_messages_are_executed_concurrently():
+async def test_messages_are_executed_concurrently_tools():
     server = FastMCP("test")
     event = anyio.Event()
     tool_started = anyio.Event()
@@ -44,3 +45,42 @@ async def test_messages_are_executed_concurrently():
             "trigger_end",
             "tool_end",
         ], f"Expected concurrent execution, but got: {call_order}"
+
+
+@pytest.mark.anyio
+async def test_messages_are_executed_concurrently_tools_and_resources():
+    server = FastMCP("test")
+    event = anyio.Event()
+    tool_started = anyio.Event()
+    call_order = []
+
+    @server.tool("sleep")
+    async def sleep_tool():
+        call_order.append("waiting_for_event")
+        tool_started.set()
+        await event.wait()
+        call_order.append("tool_end")
+        return "done"
+
+    @server.resource("slow://slow_resource")
+    async def slow_resource():
+        # Wait for tool to start before setting the event
+        await tool_started.wait()
+        event.set()
+        call_order.append("resource_end")
+        return "slow"
+
+    async with create_session(server._mcp_server) as client_session:
+        # First tool will wait on event, second will set it
+        async with anyio.create_task_group() as tg:
+            # Start the tool first (it will wait on event)
+            tg.start_soon(client_session.call_tool, "sleep")
+            # Then the resource (it will set the event)
+            tg.start_soon(client_session.read_resource, AnyUrl("slow://slow_resource"))
+
+        # Verify that both ran concurrently
+        assert call_order == [
+            "waiting_for_event",
+            "resource_end",
+            "tool_end",
+        ], f"Expected concurrent execution, but got: {call_order}"