Spawn similar dropped the session's cwd into the free-text directory hatch,
so the project picker showed nothing selected. For a worktree session that
cwd was the daemon-made checkout, and the worktree toggle defaulted on, so
the clone asked for a worktree of a worktree.
It now seeds the picker: the cloned project's box selected, the same
worktree decision, base repo plus '+ new' when the source had a worktree.
A seeded path that matches no project falls back to the raw input showing
that path instead of an empty picker.
