Feature request: allow updating git branch display mid-session (worktree support)

Problem

When working with git worktrees created mid-conversation, the UI continues showing the branch from the primary working directory (set at session start). There's no way to update the displayed branch to reflect the active worktree's branch.

Use case

My project is a Unity game with ~3.3 GB of binary assets. Creating a full worktree for each parallel task is too slow and wastes too much disk space. Instead, I use sparse worktrees that check out only source files (~7 MB of .cs files), which makes parallel agent work practical.

The workflow:

1. Start a Claude Desktop session from the main project directory (on main)
2. Ask Claude to create a sparse worktree with a new branch via a script
3. All subsequent work happens in the worktree on the new branch

The problem is that the UI keeps showing main for the entire session, even though all git operations are happening on a different branch in the worktree. There's no MCP tool or programmatic way to update the displayed branch mid-session.

Suggestion

Allow updating the primary working directory or at least the displayed git branch during a conversation — e.g., via a tool call, MCP, or automatic detection when git commands consistently target a different worktree.