Account zone is world-independent: avatar stays in Record world

Creator on the live build: 'why do you make the youtube user icon go away?'
The TASK 42 one-surface bar had scoped the account zone to Stream only
('Record world has no YouTube identity at all'), so arming REC dropped the
avatar and the bar height bounced with it ('really fucking annoying').

Fix: ShowSignInButton / ShowAvatarButton are now plain !IsConnected /
IsConnected — app-level identity, present in both worlds, so the right
column never pops in/out and the bar height stays pinned. Test remains a
child of Stream (still stream-armed AND signed-in).

TopBarModeTests updated to the new contract: signed-out Record world shows
Sign In; flipping back to REC keeps the avatar. PillRadioTests untouched
(it only exercises the ON-AIR face). Docs corrected in-place (ai.md state
model, TASK 42 scope). Gate: clean build 0-warnings, 316/316, scope passed.

TASKS/task-42-top-bar-redesign.md

@@ -21,7 +21,10 @@ world is the whole bar; the other world never exists on screen.
 - **Mode switch:** one segmented **REC|ON-AIR** toggle (former two pills are a
   binary, radio-exclusive decision). Going back = one tap on the other segment.
   Idle-only; while running the switch retires.
-- **Record world:** `switch + Start Recording`. **No YouTube identity at all.**
+- **Record world:** `switch + Start Recording`. **No Test — stream actions don't
+  exist here.** The account zone IS present (2026-09-23 correction, creator
+  "why do you make the youtube user icon go away?"): the avatar / Sign In are
+  **world-independent**, keeping the right column — and the bar height — pinned.
 - **Stream world:** `switch + Go Live + Test` and the **account zone** on the right
   (Sign In while signed-out — the pending sequence step rendered exactly when
   needed; the avatar once connected, right-click = Change Account/Logout).