Fix append last message in a_run_chat before termination check (#3561)

[wrenevens]

Why are these changes needed?

When using a_initiate_chat with a GroupChat of multiple agents,
the last agent's message was missing from the response history.

Root cause: in a_run_chat, the termination check happened BEFORE
broadcasting the message to all agents, causing the loop to exit
before the last message was appended to chat history.
The sync run_chat does not have this issue.

Changes made to bring a_run_chat in line with sync run_chat:

• Moved termination check to AFTER the broadcast
• Combined the two separate break conditions into one
• Added self._last_speaker = speaker which was missing in async
• Added NoEligibleSpeaker exception handling missing in async

Related issue number

Closes #3561

Checks

• [ x] I've included any doc changes needed for https://microsoft.github.io/autogen/. See https://github.com/microsoft/autogen/blob/main/CONTRIBUTING.md to build and test documentation locally.
• [x ] I've added tests (if relevant) corresponding to the changes introduced in this PR.
• I've made sure all auto checks have passed.

[wrenevens]

@microsoft-github-policy-service agree