[FEATURE] VS Code extension: show workspace / worktree / branch in the session panel (parity with Desktop composer chips)

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When running multiple Claude Code sessions side-by-side in VS Code (split editor groups), there is no visible indication of which project directory, git worktree, or branch each session is operating on. Sessions in different worktrees of the same repo look identical.

This makes it easy to give instructions to the wrong session, and hard to reason about which session's changes land on which branch - precisely the situation that worktree-based parallel workflows create. The project directory also determines which project-level skills and CLAUDE.md a session loads, so its invisibility causes real confusion, not just cosmetic doubt.

Proposed Solution

Render the session's workspace context as a compact persistent line in the VS Code session panel - above or below the chat input box - showing at minimum:

• project directory (basename) - to identify where e.g. skills are pulled from
• git worktree name, when the session is in one
• current branch

The Desktop app already renders exactly these as composer-footer chips (referenced in #85195), so this is a parity request: reuse that design in the VS Code webview. The underlying data already exists per-session - it is in the statusLine stdin JSON (workspace.project_dir, workspace.git_worktree, worktree.branch).

Alternative Solutions

• Rendering the user-configured statusLine command output in the panel (the VS Code counterpart of #41456) would be the fully general solution; the chips proposed here are the minimal subset that solves the split-view identity problem.
• Current workarounds, all inadequate:
• Manually renaming session tabs via "Rename Session Tab" - manual, and goes stale on branch switch.
• A third-party extension piggybacking on the statusLine command - fragile, and cannot render inside the panel.
• Keeping only one session open - defeats the point of worktrees.

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

1. Open a repo, start session A in the main checkout on main.
2. Create a worktree for feature-x, start session B there; split the two session tabs side by side.
3. Both panels are now visually identical. Prompting "commit and push" in the wrong panel pushes to the wrong branch.
4. With this feature, each panel would show e.g. myrepo ⎇ main and myrepo ⊞ feature-x ⎇ feature-x, making the sessions distinguishable at a glance.

Additional Context

Split view with 2–3 concurrent sessions in separate worktrees is the motivating workflow. The Desktop chips occasionally desync (#85195, #85114) - if this ships for VS Code, sourcing the chips from the same live session state as the statusLine JSON would avoid that class of bug.

Why this is not a duplicate (for triage): I searched existing requests; the closest matches all target a different surface or a different feature:

• #43666 - asks for improvements to the sidebar session list (grouping sessions by worktree, status indicators, inline session controls, notifications). This request asks for one thing only and on a different surface: worktree/branch context inside the individual session panel itself, next to the chat input, where you look while typing. A session-list overview does not help when two panels are open side by side; closed as stale, and its scope did not include the in-panel display.
• #41456 - statusline rendering in the Desktop app, not the VS Code extension, and the general statusline feature rather than this minimal subset of workspace, worktree and branches.
• #85195 / #85114 - bug reports about the Desktop app's existing composer chips, which are the parity precedent for this request, not the request itself.
• #83040 - Desktop sidebar grouping by worktree; again the overview surface, not the session panel.
• #58189 - Asks for something entirely different.