[Misc] Remove deprecated names (#10817)

Signed-off-by: DarkLight1337 <tlleungac@connect.ust.hk>

vllm/engine/llm_engine.py

@@ -10,7 +10,7 @@ from typing import Sequence as GenericSequence
 from typing import Set, Type, Union, cast, overload
 
 import torch
-from typing_extensions import TypeVar
+from typing_extensions import TypeVar, deprecated
 
 import vllm.envs as envs
 from vllm.config import (DecodingConfig, LoRAConfig, ModelConfig,
@@ -719,7 +719,8 @@ class LLMEngine:
     def stop_remote_worker_execution_loop(self) -> None:
         self.model_executor.stop_remote_worker_execution_loop()
 
-    @overload  # DEPRECATED
+    @overload
+    @deprecated("'inputs' will be renamed to 'prompt")
     def add_request(
         self,
         request_id: str,