[Session] Fix session idle timeout after rejected requests (#39035)

Co-authored-by: Byron Hsu <byron+per@periodiclabs.ai>
Co-authored-by: Manik Singhal <3400497+Manikvsin@users.noreply.github.com>

python/sglang/srt/session/session_controller.py

@@ -208,7 +208,6 @@ class Session:
         eos_token_ids=None,
     ):
         assert req.session_params is not None
-        self.last_active_time = time.monotonic()
         session_params = req.session_params
 
         last_req_node = None
@@ -325,9 +324,11 @@ class Session:
         if abort:
             new_req.set_finish_with_abort(abort_message)
         elif self.streaming:
+            self.last_active_time = time.monotonic()
             # req_nodes is NOT updated here — finish_req() handles it.
             self._inflight = True
         else:
+            self.last_active_time = time.monotonic()
             new_req_node = SessionReqNode(new_req, last_req_node)
             self.req_nodes[req.rid] = new_req_node