Fix an error in the type annotation

vllm/engine/async_llm_engine.py

@@ -2,8 +2,8 @@
 import time
 import weakref
 from functools import partial
-from typing import (Any, AsyncGenerator, Callable, Dict, Iterable, List,
-                    Mapping, Optional, Set, Tuple, Type, Union, overload)
+from typing import (Any, AsyncGenerator, Callable, Coroutine, Dict, Iterable,
+                    List, Mapping, Optional, Set, Tuple, Type, Union, overload)
 from weakref import ReferenceType
 
 import vllm.envs as envs
@@ -812,7 +812,7 @@ async def run_engine_loop(engine_ref: ReferenceType):
     # This method does not need to be async, but kept that way
     # for backwards compatibility.
     @overload  # DEPRECATED
-    async def add_request(
+    def add_request(
         self,
         request_id: str,
         *,
@@ -822,11 +822,12 @@ async def add_request(
         lora_request: Optional[LoRARequest] = None,
         trace_headers: Optional[Mapping[str, str]] = None,
         prompt_adapter_request: Optional[PromptAdapterRequest] = None,
-    ) -> AsyncGenerator[Union[RequestOutput, EmbeddingRequestOutput], None]:
+    ) -> Coroutine[None, None, AsyncGenerator[Union[
+            RequestOutput, EmbeddingRequestOutput], None]]:
         ...
 
     @overload
-    async def add_request(
+    def add_request(
         self,
         request_id: str,
         prompt: PromptType,
@@ -835,7 +836,8 @@ async def add_request(
         lora_request: Optional[LoRARequest] = None,
         trace_headers: Optional[Mapping[str, str]] = None,
         prompt_adapter_request: Optional[PromptAdapterRequest] = None,
-    ) -> AsyncGenerator[Union[RequestOutput, EmbeddingRequestOutput], None]:
+    ) -> Coroutine[None, None, AsyncGenerator[Union[
+            RequestOutput, EmbeddingRequestOutput], None]]:
         ...
 
     @deprecate_kwargs(