Fix ChatResponseUpdate.Clone dropping ContinuationToken

[dfedoryshchev]

ChatResponseUpdate.Clone() assigns every settable property on the type except ContinuationToken, so the token is silently dropped from the clone. The doc comment says the result is "a new ChatResponseUpdate object with the same property values as the current instance", and ContinuationToken predates Clone(), so this reads as an omission rather than a deliberate exclusion.

It is reachable in the box. ImageGeneratingChatClient.GetStreamingResponseAsync clones an update whenever it rewrites that update's contents, and yields the clone in place of the original, so for those updates the consumer sees ContinuationToken == null. The remarks on ChatResponseUpdate.ContinuationToken tell callers to pass the token from the latest received update to ChatOptions.ContinuationToken in order to resume an interrupted background stream, which a clone cannot support.

Fix: copy ContinuationToken in Clone().

Validation: extended the existing Clone_CreatesShallowCopy test to set and assert ContinuationToken. Against unmodified sources it fails with

Assert.Same() Failure: Values are not the same instance
Expected: ResponseContinuationToken { }
Actual:   null

and passes with the change. Microsoft.Extensions.AI.Abstractions.Tests: 1642 passed, 0 failed, 1 skipped. Microsoft.Extensions.AI.Tests: 761 passed, 0 failed.

Microsoft Reviewers: Open in CodeFlow

[dfedoryshchev]

@dotnet-policy-service agree