Controlled pagination pill with lock & fit-scroll

Make the floating pagination pill a controlled component and add lock/fit-aware scroll behavior. UnifiedPagination now accepts activeIndex and onDominantSectionChange, reports observer-determined dominant section (parent may ignore when locked) and only shows/hides based on footer visibility. HomePage implements controlled state (activeIndex, lockedTo) with Prev/Next/jump locking, release on wheel/touch/key or 30s safety timeout, and dot clicks that always navigate and release locks. Extracted scroll math to src/lib/utils/paginationScroll.ts (decideScrollForPageChange) so paging avoids scrolling when a section fits below the sticky header and clamps targets; added unit tests and updated component tests and docs to reflect the new behavior. Removed now-unused onPageChange prop from HomeSection.

src/components/home/HomeSection.tsx

@@ -89,7 +89,6 @@ interface HomeSectionProps {
   categoryName: string | null;
   colorIndex: number;
   page: number;
-  onPageChange: (page: number) => void;
   sectionRef: React.RefObject<HTMLElement | null>;
   cardSize: number;
   squareCovers: boolean;
@@ -226,7 +225,6 @@ export function HomeSection({
   categoryName,
   colorIndex,
   page,
-  onPageChange,
   sectionRef,
   cardSize,
   squareCovers,