Feature request: Chrome-style tabs and tab groups for managing multiple sessions

As a heavy Claude Code (desktop) user I often run several long-lived sessions in parallel — e.g. one driving browser automation + GPU transcription pipelines, another doing backend work on the same repo, another for a different project.

Today, switching between conversations means navigating a flat sidebar/list. It gets painful when:

• You have 3+ active sessions and need to hop between them quickly while background tasks notify.
• Sessions belong to different mental "projects" (e.g. "content pipeline", "prod bugfixes", "experiments") but the UI shows them as one undifferentiated list.
• You want to keep a long-running session visible/pinned while working in another.

Suggestion: adopt the Chrome tab model:

• Tabs across the top for open sessions — click to switch, drag to reorder, middle-click to close.
• Tab groups (named + colored, collapsible) to cluster related sessions, exactly like Chrome's tab groups.
• Pinned tabs for always-on sessions.
• Optional: keyboard shortcuts (Ctrl+Tab / Ctrl+1-9) matching browser muscle memory.

This would make multi-session workflows dramatically more navigable, and the interaction model is already familiar to every user.