Ok here is what worked eventually:

On socketio definition

socketio = SocketIO(app, cors_allowed_origins="*", async_mode='threading')

(I did not have the async_mode set)

And then when initialising:

if __name__ == '__main__':
    socketio.start_background_task(start_stream_consumer, r, emit_leaderboard_updates)
    socketio.run(app, debug=True)

That seems to do the trick