[FEATURE] Desktop Code tab: allow custom display names for project groups in the sidebar

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

In the Code tab sidebar, sessions are grouped by folder and each group is labeled with the folder name. The only way to change the label is to rename the folder, which breaks every absolute path that scripts, settings and hooks depend on.

The per-group "+" button (new session in that folder) is excellent, and it's the reason I don't want to switch to custom groups.

### Proposed Solution

Allow renaming a group's display name from the sidebar (e.g. right-click > Rename), without touching the folder on disk. The per-group "+" button should keep working exactly as it does today.

### Alternative Solutions

- Renaming the folder: breaks absolute paths in scripts, settings and hooks.
- Custom groups: works for labels, but I lose the per-group "+" button and have to file every new session by hand.

### Priority

Low - Nice to have

### Feature Category

Other

### Use Case Example

I use two folders on the same SSH host: one for a read-only reviewer agent (sandboxed, deny rules) and one for an executor agent. The folder names ("auditor", "docs-repo") don't say which role each group is. A display name like "Auditor" / "Executor" would make it obvious at a glance and reduce the risk of starting a session in the wrong one.

### Additional Context

Related: #80187 asked for the same thing. It was auto-closed as stale, not rejected, so I'm opening a fresh request to show there is still interest.

The issue names no files, tests, or entry points. Start by locating the Desktop Code tab's sidebar and the data that persists project-group metadata; define how a display name is stored, renamed, and preserved while folder-based grouping and the per-group "+" action continue to work.

Written by the indexing model from the issue text.