Code tab missing project management that exists in Chat and Cowork tabs

Description

In the Claude Code desktop app, the Chat and Cowork tabs have a project management feature in the left sidebar that allows organizing sessions by project. However, the Code tab does not have this feature — only a flat list of recent sessions is shown.

Expected Behavior

The Code tab should have the same project/folder-based organization in the left sidebar as the Chat and Cowork tabs, allowing users to group and manage coding sessions by project (similar to how Codex organizes projects).

Current Behavior

• Chat tab: has project management ✓
• Cowork tab: has project management ✓
• Code tab: only shows recent sessions, no project management ✗

Why This Matters

When working on multiple codebases, it's difficult to navigate between projects using only a flat recent-sessions list. Project-based organization would significantly improve workflow management for users working across multiple repositories or projects.