[FEATURE] Desktop: sidebar tool to reorder custom groups, so Claude can do it on request

Context

Custom sidebar groups can now be reordered by drag and drop in the Code tab. Claude's built-in sidebar tools can already create, rename and delete groups and move sessions between them, but they cannot change the order of groups.

So when I ask Claude to tidy my sidebar, it can create a group like "Coordination" but cannot put it where it belongs (directly below Pinned). I have to drag it myself afterwards.

Request

A sidebar tool to set a group's position, for example:

• move_group(group_id, position) with a target index, or
• move_group(group_id, before | after: other_group_id)

so that a prompt like "put Coordination right below Pinned" works end to end.

Why it matters

With 35 groups, order is how I find things. Claude already maintains the groups for me (creating, merging, filing sessions); without ordering, every tidy-up still ends with manual dragging.

Related

• #70104 added drag-to-reorder for groups by hand (shipped). This request is the tool counterpart, so Claude can do the same on request.
• #83307 asked for the same reordering and was closed as a duplicate of #70104.
• #101307 (per-group view controls on custom groups)