Codex Desktop: add an inline project-name filter to the Projects sidebar

What feature would you like to see?

Add a small inline search icon beside the Projects heading in the Codex Desktop sidebar.

Clicking it should expand a compact input that filters local Codex Projects by:

• project display name
• workspace/root-folder basename
• full local path

Suggested keyboard behavior:

• ↑ / ↓ selects a result
• Enter opens the selected project
• Esc clears and closes the filter

Why this matters

Codex is designed for running work across many local projects. Heavy users quickly accumulate dozens of repositories and workspace roots. Once the list exceeds one screen, switching projects becomes a scrolling task.

The dedicated Projects page is useful for project management. High-frequency project switching still happens in the sidebar, so search should be available at that point of action.

Folders, subfolders, profiles, and workspaces help users classify projects. Inline search gives users immediate retrieval when they already know part of the project name or path.

Implementation scope

This can remain a lightweight client-side feature:

1. Reuse the existing local project catalog and project-name/path matching logic.
2. Filter the rendered sidebar project rows without changing project state.
3. Preserve the current project ordering and collapsed state after the query is cleared.
4. Search the full loaded project catalog so results are not limited to currently visible rows.

No model, agent-loop, filesystem, or backend behavior needs to change.

Related requests

This complements the broader workspace and folder proposals in:

• #18329
• #19131

Those requests focus on organizing large project collections. This request focuses on quickly locating one local Codex Project from the sidebar.

Begin at the Codex Desktop sidebar's Projects heading and trace the existing local project catalog and project-name/path matching logic mentioned in the issue. Done means the sidebar can filter the full loaded catalog by display name, workspace or root-folder basename, and full local path, with the specified keyboard behavior and preserved ordering after clearing.