fix: Add explicit [DONE] signal to SSE stream endpoint

Fixes issue where /run_sse endpoint sometimes fails to close
the SSE connection after the model's final response, causing
client-side hangs.

Changes:
- Add 'data: [DONE]' termination signal after all events streamed
- Send [DONE] in error path as well for consistency
- Update test to filter out [DONE] signal

Author: DineshThumma9

src/google/adk/cli/adk_web_server.py

@@ -1557,6 +1557,9 @@ async def event_generator():
                     "Generated event in agent run streaming: %s", sse_event
                 )
                 yield f"data: {sse_event}\n\n"
+
+          # Send termination signal after all events have been streamed
+          yield "data: [DONE]\n\n"
         except Exception as e:
           logger.exception("Error in event_generator: %s", e)
           # Yield a proper Event object for the error
@@ -1570,6 +1573,7 @@ async def event_generator():
               "data:"
               f" {error_event.model_dump_json(by_alias=True, exclude_none=True)}\n\n"
           )
+          yield "data: [DONE]\n\n"
 
       # Returns a streaming response with the proper media type for SSE
       return StreamingResponse(

tests/unittests/cli/test_fast_api.py

@@ -1005,7 +1005,7 @@ async def run_async_with_artifact_delta(
   sse_events = [
       json.loads(line.removeprefix("data: "))
       for line in response.text.splitlines()
-      if line.startswith("data: ")
+      if line.startswith("data: ") and line != "data: [DONE]"
   ]
 
   assert len(sse_events) == 2