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

[SergeyMenshykh]

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.

Related: #1760