[Core] Enable StatLogger in LLMEngine (#28020)

Signed-off-by: Zhuohan Li <zhuohan123@gmail.com>

Author: zhuohan123

vllm/v1/engine/llm_engine.py

@@ -58,11 +58,6 @@ def __init__(
         use_cached_outputs: bool = False,
         multiprocess_mode: bool = False,
     ) -> None:
-        if stat_loggers is not None:
-            raise NotImplementedError(
-                "Passing StatLoggers to LLMEngine is not yet supported."
-            )
-
         self.vllm_config = vllm_config
         self.observability_config = vllm_config.observability_config
         self.model_config = vllm_config.model_config