With a vertical bar present, the Duo header moved every bottom toolbar
item into the trailing navigation items, so UIKit could no longer keep
the top and bottom groups apart. It also copied the thread filter into
every detail rail, forced the Mail-style search items to horizontal-only
(UIKit hides those when no horizontal bar is present), and the unfolded
Duo showed Compose twice: in the sidebar toolbar and the thread header.

- Bottom toolbar items stay toolbar items. UIKit places them at the
  bottom of the vertical bar, separated from the navigation items.
- The thread filter stays with the list, as the chips at its top. The
  rail copy and its option plumbing are removed.
- The Duo list searches from its bottom toolbar beside Compose in every
  pose, so the sidebar header holds only the title and Settings.
- Mail-style search items use automatic axis behavior. Their fixed
  spaces remain only where there is no vertical bar.
- The Duo thread header shows New task only while the sidebar is
  hidden, so exactly one Compose is visible.
- HomeHeader's iOS toolbar path was unreachable behind the workspace
  toolbar and is removed.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>