[BUG] Completed scheduled task sessions don't appear in the Today sessions list (macOS)

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

When a scheduled task fires and completes in the Claude Code desktop app, the resulting session only appears under Scheduled > Tasks > Your Task > Click on latest in "Runs". It does not show up in the main Today sessions list alongside regular chat sessions.
This makes it hard to find the output of recurring tasks (e.g. a daily PR digest) — you have to remember the task exists, navigate to the Scheduled panel, and drill into the specific task to see its latest run, instead of just scanning Today like any other session.

What Should Happen?

Completed scheduled task sessions should also appear in the Today sessions list (ideally with a small icon/badge indicating they originated from a scheduled task), so users can find recent task outputs in the same place as their normal session history.

Error Messages/Logs

Steps to Reproduce

1. Create a recurring scheduled task (e.g. daily cron at 9:00 AM that summarizes open PRs).
2. Wait for it to fire, or trigger it manually.
3. Open the Today sessions view in the sidebar.
4. Observe that the completed task session is not listed.
5. Navigate to Scheduled > Tasks > [task name] — the session is there.

Claude Model

None

Is this a regression?

No, this never worked

Last Working Version

_No response_

Claude Code Version

Desktop Claude 1.1617.0 (8d6345) - Claude Code Cli v2.1.101

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

Terminal.app (macOS)

Additional Information

_No response_