fix(acp): stop emitting user_message_chunk during session/prompt turn

[RAIT-09]

Issue for this PR

Closes #21708

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

Removes the user_message_chunk emission from the live message.part.updated handler during session/prompt turns.

Per the ACP spec, user_message_chunk should only be sent during session/load or session/fork to replay conversation history. #18625 added this emission on the live prompt path to align output between live and replay paths, but ACP clients already know the message they sent — the echo causes duplicate display.

This change only affects the live prompt path. session/load and session/fork replay behavior is unchanged.

How did you verify your code works?

• Connected to the patched build via Obsidian Agent Client and Zed Editor over ACP
• Confirmed user messages are no longer duplicated on prompt
• Confirmed session/load still correctly replays full conversation history including user messages
• typecheck passes, existing tests pass

Screenshots / recordings

Before:

After:

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR