fix: hot reload agents for adk web

Co-authored-by: Yifan Wang <wanyif@google.com>
PiperOrigin-RevId: 908496612

Author: wyf7107

src/google/adk/cli/adk_web_server.py

@@ -1889,6 +1889,7 @@ def _set_telemetry_context_if_needed(runner: Runner):
 
     @app.post("/run", response_model_exclude_none=True)
     async def run_agent(req: RunAgentRequest) -> list[Event]:
+      self.current_app_name_ref.value = req.app_name
       runner = await self.get_runner_async(req.app_name)
       _set_telemetry_context_if_needed(runner)
       try:
@@ -1910,6 +1911,7 @@ async def run_agent(req: RunAgentRequest) -> list[Event]:
 
     @app.post("/run_sse")
     async def run_agent_sse(req: RunAgentRequest) -> StreamingResponse:
+      self.current_app_name_ref.value = req.app_name
       stream_mode = StreamingMode.SSE if req.streaming else StreamingMode.NONE
       runner = await self.get_runner_async(req.app_name)
       _set_telemetry_context_if_needed(runner)
@@ -2089,6 +2091,7 @@ async def run_agent_live(
         return
 
       await websocket.accept()
+      self.current_app_name_ref.value = req.app_name
       runner_for_context = await self.get_runner_async(app_name)
       _set_telemetry_context_if_needed(runner_for_context)