Desktop: "Suggested task" chip card always defaults to "Start with worktree" - saved spawn-target preference regressed (~Jul 21)

Describe the bug

Since ~2026-07-21 the "Suggested task" popup card in Claude Code Desktop (background task suggestions created via the spawn_task tool) always shows "Start with worktree" as the primary action of its split button. "Start locally" only exists in the dropdown, and the choice is not remembered - the next chip is back to "Start with worktree".

Until ~Jul 20 the primary action reflected the persisted target preference (epitaxy-spawn-task-target-v2, values local/worktree/cloud/here, menu items with checkmarks). Users who had chosen "Start locally" got local starts by default. That preference is still stored in claude_desktop_config.json (preferences.epitaxyPrefs) but the card no longer reads it, and a selection made in the dropdown is no longer persisted anywhere.

Steps to reproduce

1. Have any session create a task suggestion via the spawn_task tool.
2. On the chip card, open the dropdown next to "Start with worktree" and pick "Start locally".
3. Let the next chip appear.
4. The primary action is "Start with worktree" again - the explicit choice was not persisted (reproduced 10+ times).

Expected behavior

Remember the last explicitly chosen start target (the pre-Jul-21 behavior), or offer a setting to disable defaulting to worktrees for local sessions.

Environment

• Claude Desktop 1.24012.9 (Windows 11 Pro)
• Web frontend build 2026-07-25
• Bundled Claude Code CLI 2.1.219