[Feature Request] Desktop app: full session list ("Show all") doesn't display or allow managing custom group assignment

## Preflight Checklist
- [x] I have searched existing issues and this hasn't been reported yet (closest related: #81914, #69105, #61553, #78812, #79810, #86843, #94527 — none cover this specific gap)
- [x] This is a single feature request
- [x] I am using the latest version of Claude Desktop

## What's Wrong?

In the Claude Desktop app, the main sidebar supports "Group by → Custom groups" to organize chat sessions. This works fine for sessions visible in the sidebar's recent-activity window.

However, older sessions that scroll out of that window are only reachable via the "Show all" / "Conversations et tâches" full-list view. In that view:
- No indication of which custom group (if any) a session belongs to
- No way to assign a session to a group, or move it between groups

As a result, any older/ungrouped session that falls out of the sidebar's recent window becomes effectively orphaned: invisible in its group context, and impossible to file into a group without first surfacing it back into the main sidebar (if even possible).

## Expected Behavior

The full session list view should show each session's current group (or "Ungrouped"), and allow assigning/moving a session to a custom group directly from that view — matching the functionality already available in the main sidebar.

## Steps to Reproduce

1. Create several custom groups in the sidebar (Group by → Custom groups)
2. Let enough sessions accumulate that some scroll out of the sidebar's visible window
3. Click "Show all" / open the full "Conversations et tâches" list
4. Observe: no group column/label, no way to assign a session to a group from this view

## Environment

- Claude Desktop app
- macOS

Start by locating the Claude Desktop full session list view and the existing sidebar custom-group assignment behavior; the issue names no files, tests, or entry points. Compare the two views and determine how sessions and group assignments are represented. Done means the full list shows each session's group or “Ungrouped” and supports assigning or moving sessions between custom groups.

Written by the indexing model from the issue text.