fix(directory-picker-browse): advertise the path editor and walk the panes with the draft

The Select Workspace Directory dialog hid its one route into typing a path
behind an invisible click target, and once the editor opened the panes stayed
on whatever level was listed when it opened — so the typed text and the list
under it disagreed for the whole edit.

The edit zone now carries a pencil glyph at the bar's right edge and lights in
the editor's own footprint on hover/focus (the bar keeps one height across the
swap). While editing, the panes follow the draft: a directory part no pane
lists is scanned after a 250ms rest and lands in place, so typing deeper
descends and erasing segments steps back up without leaving the editor, and a
final segment nobody matches releases the prefix filter instead of emptying
the pane it is being spelled into. The draft-following scan is speculative and
silent on failure; Enter still owns the view from submission until landing and
remains the only path that surfaces an error.

apps/web/tests/snapshots/workspace-management/directory-browser.expected.md

@@ -4,7 +4,8 @@
     - button "Home"
     - img
     - button "browse-golden"
-  - button "Edit path"
+  - button "Edit path":
+    - img
   - list:
     - listitem:
       - button "adopted":