[FEATURE] Claude Desktop: add "Move to group" to the Recents page (older sessions can't be grouped)

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

This is about the Claude Desktop app (macOS, version 2.31226.1 (857652)), not the CLI.

In the desktop sidebar, sessions can be organised into groups: a session's ⋮ menu (or right-click) offers "Move to group". The Recents page (Active tab), which lists all sessions, has a ⋮ menu with only Select, Pin, Mark as unread, Rename and Delete.

Older sessions that are no longer listed in the sidebar can only be reached from the Recents page, so there is no way to move them into a group. Sorting an existing history into groups is therefore impractical.

Proposed Solution

• Add "Move to group" to the ⋮ menu of each row on the Recents page.
• Add "Move to group" as a bulk action in Select mode, so several sessions can be grouped at once.
• Ideally, allow dragging a row from the Recents page onto a group in the sidebar.

Alternative Solutions

What I tried:

• Select mode on the Recents page: no group action for the selection.
• Drag-and-drop from the Recents page onto a sidebar group: no effect.
• Pinning the session from the Recents page: does not make "Move to group" available.
• Opening the session so that it shows in the sidebar, then using the sidebar menu: works, but it changes the session's recency and has to be done one session at a time.

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

1. I create a few groups in the sidebar and want to sort my existing history into them.
2. For recent sessions, ⋮ → Move to group in the sidebar works.
3. For older sessions, I open the Recents page: the ⋮ menu there has no "Move to group", and neither Select mode nor drag-and-drop lets me assign a group.

Additional Context

Same request as #99627, which was closed automatically by the github-actions bot as not related to Claude Code. Refiling because this repository does track Claude Desktop sidebar group issues (e.g. #93210, #58193).