feat(tui): add worktree support for session creation

[abrekhov]

Summary

• Adds worktree (workspace) support to the TUI, matching the Web UI's existing capability
• Users can create isolated git worktrees per session via the /workspace slash command (aliases: /worktree, /sandbox)
• Sessions created in a worktree use a dedicated SDK client targeting that worktree's directory, ensuring full isolation

Changes

• context/sync.tsx — Track sandboxes list in sync store, fetch via sdk.client.worktree.list(), refresh on project.updated events
• context/sdk.tsx — Add createClient(directory) helper to create SDK clients targeting specific worktree directories
• component/dialog-worktree.tsx(new) — Worktree selector dialog with options: main workspace, existing sandboxes, create new
• routes/home.tsx — Workspace state persisted via KV, workspace label in footer bar
• component/prompt/index.tsx — Worktree-aware submit: creates worktree via API if needed, routes session/prompt calls through worktree-specific client
• component/dialog-session-list.tsx — Shows [workspace-name] for sessions belonging to a worktree
• app.tsx — Register /workspace slash command (only for git projects)

Testing

• bun turbo typecheck passes all 12 packages
• Follows existing patterns from Web UI (packages/app/src/components/prompt-input/submit.ts, session-new-view.tsx)

[github-actions]

Thanks for your contribution!

This PR doesn't have a linked issue. All PRs must reference an existing issue.

Please:

1. Open an issue describing the bug/feature (if one doesn't exist)
2. Add Fixes #<number> or Closes #<number> to this PR description

See CONTRIBUTING.md for details.

[github-actions]

The following comment was made by an LLM, it may be inaccurate:

Based on my search results, I found one potentially related PR:

PR #12008: fix: filter CLI sessions by current directory for worktree support

Why it might be related: This PR addresses worktree support at the CLI level by filtering sessions based on the current directory. Since the current PR (13528) adds worktree support to the TUI with directory-based session isolation, these two PRs are working on related aspects of the same worktree feature - one for CLI and one for TUI.

All other search results either returned the current PR itself (13528) or unrelated PRs about memory leaks, layouts, snapshots, etc.

[logiclogue]

Can we get this merged?

[github-actions]

Closing this pull request because it has had no updates for more than 60 days. If you plan to continue working on it, feel free to reopen or open a new PR.