[BUG] Desktop: empty custom sidebar groups vanish from the sidebar after restart but stay stored, so recreating them piles up duplicates

What happens

In the Claude desktop app's Code tab, a custom sidebar group that has no sessions in it is no longer shown after the app is restarted. The group is not deleted, though: it is still in the stored sidebar data, just not visible. Recreating it by name then leaves a second group with the same name, and the hidden one stays behind.

Steps to reproduce

1. In the Code tab sidebar, create a custom group (e.g. "Outgoing My Turn") and leave it empty, or move its last session out.
2. Quit and reopen the app.
3. The empty group is gone from the sidebar.
4. Create a group with the same name again. Repeat a few times.

Expected

An empty custom group stays visible across restarts (it is a label the user made on purpose, often a workflow stage that is empty for a while). If hiding empty groups is intended, it should be a visible setting, and creating a group with an existing hidden group's name should reuse it.

Actual

After several rounds, the sidebar's stored group list (as returned by the app's own sidebar tools, list_groups / list_sections) holds five separate groups all named "Outgoing My Turn", each with its own id and session_count: 0, plus two other empty groups. Other names are duplicated too (two "Approved", two "Cleanup"), presumably from the same loop at a time when they were empty. 23 custom groups are stored in total.

The two listings also disagree on order for the same groups (list_groups order vs list_sections order), in case that points at two stores that have drifted.

Whether the empty groups are hidden by the renderer or dropped from the view on load I can't tell from outside; the stored data is what shows they are not deleted.

Environment

• Claude desktop app 2.19675.1 (Code tab), macOS 26.6
• Local sessions

Possibly related: #79810 (custom groups disappear after switching accounts), #95979 (no way to hide empty groups).