[Desktop] Display current worktree/cwd name in app UI (statusLine equivalent)

Problem

The Claude Code desktop app does not support the statusLine setting from ~/.claude/settings.json — it's CLI-only. As a result, there is no visible indicator anywhere in the desktop UI of which working directory or git worktree the current session is operating in.

Impact

This is especially painful when using git worktrees (e.g. via the /worktree skill or manual git worktree add):

• The desktop session sidebar auto-generates labels that don't match worktree names
• Window title shows generic "Claude" with no cwd info
• After closing a session, orphan worktrees accumulate in external tools (GitKraken, git worktree list) with no way to trace which session created them
• Users have to manually grep ~/.claude/projects/<encoded-path>/*.jsonl to recover the link

Configured but ignored

A working CLI statusLine config produces useful output:

🌿 suspicious-dubinsky-2af01b · claude/suspicious-dubinsky-2af01b

This appears in the CLI bottom bar, but nowhere in the desktop window.

Request

Any one of the following would resolve this:

1. Honor statusLine in desktop — render the configured command output somewhere visible (bottom bar, header chip, or near the model badge)
2. Auto-prefix sidebar session label with worktree name — when a session is opened in a path under .claude/worktrees/<name>/, prepend (or suffix) the worktree name to the auto-generated session label in the sidebar
3. Expose sessionName in SessionStart hook output — let a SessionStart hook return {\"sessionName\": \"...\"} (alongside existing additionalContext/systemMessage/etc) so users can script their own naming convention. This is the most flexible option and unblocks custom naming for any cwd pattern, not just worktrees
4. Session ↔ worktree link in sidebar — surface the cwd on hover, and/or show worktree name as a badge on the session card

Currently the only workaround is to manually run /rename <name> inside every new session, which defeats the convenience of automatic worktree creation.

Environment

• macOS desktop app (Claude Code)
• Multiple concurrent git worktrees under <repo>/.claude/worktrees/
• Each worktree is a separate Claude Code session