feat(mobile): collapsed pill composer and mobile input redesign

Mobile composer redesign: when the keyboard is closed the input collapses
into a narrow pill (sessions, attach, placeholder, mic) with a round
new-session button that fades away on the draft screen. Model and agent
selectors move into a row above the textarea; the draft project/branch
pickers and the attachment menu become searchable bottom sheets reusing
MobileOverlayPanel; a drag handle (also available while dictating) swipes
the composer into and out of a fullscreen mode.

Keyboard-lifecycle hardening: composer controls (agent cycle, dictation
and its overlay controls) no longer steal focus and dismiss the keyboard;
overlays reopen the keyboard on close via a debounced restore chain that
survives menu-to-picker handoffs and skips the native file picker; open
overlays and dictation keep the composer expanded. Dictation starts
directly from the pill and its overlay content fades in after the shape
settles. The keyboard slide compensates the pill-to-full height change in
one motion, and the mobile highlight mirror is disabled so the caret
always matches the text layout.

packages/ui/src/components/chat/MobileAgentButton.tsx

@@ -31,7 +31,12 @@ export const MobileAgentButton: React.FC<MobileAgentButtonProps> = ({ onCycleAge
     const longPressTimerRef = React.useRef<ReturnType<typeof setTimeout> | null>(null);
     const isLongPressRef = React.useRef(false);
 
-    const handlePointerDown = () => {
+    const handlePointerDown = (event: React.PointerEvent) => {
+        // Same pattern as PermissionAutoAcceptButton: block the focus transfer
+        // iOS performs on touch so cycling the agent keeps the keyboard open.
+        if (event.pointerType === 'touch') {
+            event.preventDefault();
+        }
         isLongPressRef.current = false;
         longPressTimerRef.current = setTimeout(() => {
             isLongPressRef.current = true;
@@ -72,6 +77,7 @@ export const MobileAgentButton: React.FC<MobileAgentButtonProps> = ({ onCycleAge
             onPointerUp={handlePointerUp} // Don't use onClick - it closes mobile keyboard
             onPointerLeave={handlePointerLeave}
             onContextMenu={(e) => e.preventDefault()}
+            onMouseDown={(e) => e.preventDefault()}
             className={cn(
                 'inline-flex min-w-0 items-stretch select-none',
                 'rounded-lg',