Red dot notification persists on current conversation after task completes

[BlessedChild]

Summary

After a task is completed in a conversation, the red dot notification badge remains visible on that conversation. It only disappears after switching to a different conversation and coming back. This makes the notification behavior feel inconsistent.

Steps to reproduce

1. Start and complete a task in a conversation.
2. Observe the red dot notification badge on the current conversation in the sidebar.
3. Stay in the same conversation - notice the red dot persists.
4. Switch to another conversation, then switch back - notice the red dot is gone.

Expected behavior

The red dot should disappear immediately when the task completes in the current conversation, since the user is already viewing the results. Alternatively, the notification should clear when the user clicks on any other conversation.

Actual behavior

The red dot persists even after the task is done and the user is viewing the results. It only clears after navigating away and back to the conversation.

Suggested fix

• When a task completes in the currently active conversation, clear the red dot notification for that conversation immediately.
• Or: suppress the notification entirely for the active conversation, since the user is already seeing the result.

Screenshots

Environment

• App: Finch 1.4.4 (1169) — Desktop
• OS: macOS 26.4.1 (25E253)