[Doc] Reorganize online pooling APIs (#11172)

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

vllm/entrypoints/openai/api_server.py

@@ -406,7 +406,7 @@ async def create_embedding(request: EmbeddingRequest, raw_request: Request):
     assert_never(generator)
 
 
-@router.post("/v1/score")
+@router.post("/score")
 async def create_score(request: ScoreRequest, raw_request: Request):
     handler = score(raw_request)
     if handler is None:
@@ -423,6 +423,15 @@ async def create_score(request: ScoreRequest, raw_request: Request):
     assert_never(generator)
 
 
+@router.post("/v1/score")
+async def create_score_v1(request: ScoreRequest, raw_request: Request):
+    logger.warning(
+        "To indicate that Score API is not part of standard OpenAI API, we "
+        "have moved it to `/score`. Please update your client accordingly.")
+
+    return await create_score(request, raw_request)
+
+
 if envs.VLLM_TORCH_PROFILER_DIR:
     logger.warning(
         "Torch Profiler is enabled in the API server. This should ONLY be "