ui: prevent layout shift when mobile search overlay opens

- SearchPanel: focus input with { preventScroll: true } so the browser
  doesn't auto-scroll the underlying page when the overlay mounts.
- SearchPanel: add overscroll-contain on the scroll container so
  reaching the panel's edges does not chain into the body on Android.
- PublicLayout: lock background scroll while the mobile search overlay
  is open using the iOS-compatible position-fixed + restore pattern,
  so the page underneath cannot move at all.

src/layouts/PublicLayout.tsx

@@ -331,6 +331,35 @@ export function PublicLayout() {
     };
   }, [open]);
 
+  // Lock background scroll while the mobile search overlay is open.
+  // Uses the iOS-compatible position-fixed pattern so the underlying page
+  // doesn't move at all (overflow:hidden alone is not enough on iOS Safari).
+  useEffect(() => {
+    if (!mobileSearchOpen) return;
+    const scrollY = window.scrollY;
+    const body = document.body;
+    const prev = {
+      position: body.style.position,
+      top: body.style.top,
+      left: body.style.left,
+      right: body.style.right,
+      width: body.style.width,
+    };
+    body.style.position = "fixed";
+    body.style.top = `-${scrollY}px`;
+    body.style.left = "0";
+    body.style.right = "0";
+    body.style.width = "100%";
+    return () => {
+      body.style.position = prev.position;
+      body.style.top = prev.top;
+      body.style.left = prev.left;
+      body.style.right = prev.right;
+      body.style.width = prev.width;
+      window.scrollTo(0, scrollY);
+    };
+  }, [mobileSearchOpen]);
+
   return (
     <div className="min-h-full flex flex-col">
       <DocumentMeta />