A formula bar host is a box around the same input the in-grid editor renders, driving the same
SheetEditable, so typing in either place is one edit. The hosts differ in chrome (a name box, a
resize grip, how the ✕ / ✓ / fx buttons sit), not in behavior; this hook is the behavior.
Ending a session from here does not return focus to the grid. That spans the bar and the grid, which only the studio owns (see the editable-session focus-restore effect in EagerStudio).
Everything a formula bar host shares with the other hosts: which cell the bar shows, whether it may edit, the live session on the shared editable, and the editor element itself.