.NET: [BackagroundResponses] Allow ChatClientAgent to work with non-ChatClientAgent continuation tokens

**Context:**
As part of addressing this issue: https://github.com/microsoft/agent-framework/issues/1762, a new continuation token type specific to `ChatClientAgent` will be added. The continuation token will wrap a continuation token returned by `IChatClient` and will allow `ChatClientAgent` to add additional data that will be accessed during the stream resumption phase, together with the original continuation token which will be sent to `IChatClient` for resumption.

**ToDo:**
Update `ChatClientAgent` to accept continuation tokens of the underlying `IChatClient` type, to enable scenarios such as push notifications. In these scenarios, a host will mint (based on information from the push notification payload) a continuation token that the underlying `IChatClient` supports, and `ChatClientAgent` will pass it through to the chat client.

Start at ChatClientAgent and trace how continuation tokens are accepted and passed to IChatClient during stream resumption. Confirm the existing continuation-token contract and verify that a token minted for the underlying chat client can be resumed through ChatClientAgent without losing the agent-specific context.

Written by the indexing model from the issue text.