Codex Desktop: support nested local projects in the Projects sidebar

What variant of Codex are you using?

App / Codex Desktop

What feature would you like to see?

When one saved local project directory is physically contained inside another saved local project directory, Codex Desktop should support displaying it as a nested child project instead of forcing every project to appear at the same top level.

An anonymized example:

C:\Workspaces\Local
C:\Workspaces\Local\reader-app

Preferred sidebar structure:

Projects
└─ Local
   └─ reader-app

Today both entries appear as top-level peers. As more subprojects are added, the Projects sidebar becomes increasingly difficult to scan.

Requested behavior

• Detect directory containment automatically, or allow users to assign a parent project manually.
• Show child projects below their parent with collapse/expand controls.
• Preserve each child project's exact working directory, permissions, local environment, and project-specific configuration.
• Allow users to switch between hierarchical and flat views if desired.
• Keep project removal a sidebar-only action; it must not delete the underlying local directory.
• Support more than one nesting level where the filesystem structure warrants it.

Why this matters

Umbrella workspaces, monorepos, client workspaces, and collections of small local projects commonly contain many independent subdirectories. Separate local projects are useful for focused working directories and permissions, but representing every subdirectory as a top-level sidebar entry creates unnecessary clutter.

Users currently have to choose between:

1. one broad parent project with a clean sidebar but weaker per-project separation, or
2. many focused child projects with strict working directories but an unmanageable flat sidebar.

A nested project view would retain both organization and isolation.

Related issues

• #28692 requests general custom ordering and sidebar sections.
• #28213 requests labels, folders, and other chat organization.
• #25498 requests project management and moving threads between projects.

This request is specifically about representing saved local projects according to their parent/child directory relationship, while keeping each project operationally independent.