Verify each finding against the current code and only fix it if needed.

Inline comments:
In `@tensorrt_llm/serve/harmony_adapter.py`:
- Around line 1613-1615: The final-chunk path skips emitting the initial
assistant-role SSE chunk when output.token_ids_diff is empty; update the logic
around harmony_adapter.create_openai_streaming_response so it always emits the
assistant-role/event chunk prior to sending finish/usage chunks even if
token_ids_diff is empty—i.e., factor out or call the same assistant-chunk
emission used in the non-done path before checking output.token_ids_diff,
ensuring the code paths at the blocks around output.token_ids_diff (the call to
harmony_adapter.create_openai_streaming_response and the subsequent finish/usage
sending blocks) both produce the initial assistant-role SSE event.
- Around line 1615-1620: The code calls
harmony_adapter.create_openai_streaming_response(...) and then unconditionally
appends a terminal final_response when done=True, which can duplicate a stop
chunk if create_openai_streaming_response already produced one; update the logic
around remaining_responses and final_response in the done=True branches (the
occurrences that use remaining_responses and final_response) to short-circuit:
check whether remaining_responses already contains a terminal/stop chunk (the
same marker your streaming responses use) and if so do not append another
final_response, and apply the same fix to the duplicate block later (the similar
code around lines 1632-1649) to avoid emitting duplicate terminal stop chunks.
- Around line 214-219: The current filtering in should_filter_tools + the other
site (and harmony_output_to_openai) wrongly blocks built-in tools like
"browser", "python", and "container" when external tools are present; implement
a single helper (e.g., is_tool_allowed(request_id, func_name, tool_choice,
available_tools)) and use it in both filter locations so that: if tool_choice ==
"none" it returns false for everything; if tool_choice != "none" it always
returns true for built-ins ("browser", "python", "container"); and for
non-built-in functions it checks membership against available_tools (and
respects should_filter_tools). Update calls in the places referencing
should_filter_tools / available_tools and harmony_output_to_openai to call this
helper instead.
- Around line 205-223: The current branch opens streamed tool calls for
parser.current_channel == "analysis" but the transition logic in
process_token_batch() and process_token_batch_to_messages() only deactivates
previous tool calls when prev_channel == "commentary", causing reuse/merging of
tool_id across analysis-invocations; update both transition handlers so they
retire (set active=False) prior tool calls when prev_channel is either
"commentary" or "analysis" (i.e., check prev_channel in
("commentary","analysis")) before creating/getting a new tool call via
_get_or_create_tool_call, ensuring parser.current_channel/
current_channel_state/_get_or_create_tool_call don't reuse an old tool_id from
the other channel.