This PR fixes a chat bug where queued messages could seem to disappear when switching between chats.

Before:

• If Chat A had queued follow-up messages and you switched to Chat B, Chat A could finish in the background but only the assistant replies would show later.
• The user messages for those queued follow-ups could be missing.
• If you switched back to Chat A very quickly while it was still running, queued items could appear to get cleared from the UI.

Changes:

• Background chat processing now saves queued user messages properly, not just assistant replies.
• Chat switching no longer drops in-between events during the handoff back to an active chat.
• The queue UI no longer clears itself just because a temporary refresh fails.

After :