Feature request: Tabbed/multi-project sessions with a project 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

Currently, switching between projects requires either restarting Claude Code in a new directory (losing conversation context) or using /add-dir (which adds scope but doesn't give a clean per-project workspace). There's no way to keep several project sessions open in parallel and switch between them quickly.

### Proposed Solution

Support tab-like sessions, each bound to its own project directory, plus a sidebar/menu listing recently used projects for quick switching — similar to browser tabs or an IDE's recent-projects list. This would let users:
Keep multiple project contexts alive at once without losing history
Switch between projects with one click/command instead of restarting
See a persistent list of recently used project folders
Related issues: #19903, #38308, #60151, #1628, #3473 (all about mid-session working directory changes)

### Alternative Solutions

_No response_

### Priority

Critical - Blocking my work

### Feature Category

CLI commands and flags

### Use Case Example

_No response_

### Additional Context

_No response_

Start by reading the existing /add-dir command and the related issues #19903, #38308, #60151, #1628, and #3473 to understand current directory and session behavior. The feature is done when multiple project-bound sessions can remain open, users can switch between them without losing conversation history, and recently used project folders are listed for quick access.

Written by the indexing model from the issue text.