.NET: [BackagroundResponses] ChatClientAgent.RunStreamingAsync input messages loss on first run failure

When Background Responses are enabled, if ChatClientAgent.RunStreamingAsync fails during the first run, the input messages provided to the run will never be added to the thread (client-side only; the server-side ones are added by the server). The context provider won't receive those updates either. This will leave the thread and context provider in an invalid state.