Keep settled mobile sidebars hidden under UI load

The earlier ghost-open fix gated re-commits on a settle counter, but on
Fabric that doesn't hold: Reanimated re-applies its own (stale) animated
props over React's committed props on every commit, so a settled-closed
sidebar still reappears after a heavy commit (e.g. a long thread mounting
or a message send) — reanimated#9635. No committed transform/opacity
value can win while a useAnimatedStyle is attached.

Split ownership instead: React owns whether the overlay exists, the
worklet owns its motion. display lives on the plain wrapper View that
Reanimated never touches, so a hidden overlay stays hidden regardless of
what the animated props revert to. An open gesture flips an overlayPeek
flag to reveal the panel before the store updates; a short close grace
keeps it displayed until the close animation finishes.

Residual: a heavy commit landing mid-close-animation can still flash the
panel until the animation settles — transient, not the previous permanent
wedge.

packages/app/src/hooks/use-explorer-open-gesture.ts

@@ -20,6 +20,7 @@ export function useExplorerOpenGesture({ enabled, onOpen }: UseExplorerOpenGestu
     windowWidth,
     animateToOpen,
     animateToClose,
+    setOverlayPeek,
     isGesturing,
     gestureAnimatingRef,
     openGestureRef,
@@ -93,6 +94,8 @@ export function useExplorerOpenGesture({ enabled, onOpen }: UseExplorerOpenGestu
         })
         .onStart(() => {
           isGesturing.value = true;
+          // The overlay is display:none while closed; reveal it for the drag.
+          runOnJS(setOverlayPeek)(true);
         })
         .onUpdate((event) => {
           // Right sidebar: start from closed position (+windowWidth) and move towards 0.
@@ -122,6 +125,7 @@ export function useExplorerOpenGesture({ enabled, onOpen }: UseExplorerOpenGestu
         })
         .onFinalize(() => {
           isGesturing.value = false;
+          runOnJS(setOverlayPeek)(false);
         }),
     [
       enabled,
@@ -131,6 +135,7 @@ export function useExplorerOpenGesture({ enabled, onOpen }: UseExplorerOpenGestu
       mobilePanelState,
       animateToOpen,
       animateToClose,
+      setOverlayPeek,
       isGesturing,
       openGestureRef,
       leftOpenGestureRef,