style: apply analyzer lint fixes across lib

Initializing formals, unawaited() on fire-and-forget futures, unused
import removal, wildcard params, and mounted vs context.mounted.

lib/mixins/paginated_item_loader.dart

@@ -47,7 +47,7 @@ mixin PaginatedItemLoader<T, W extends StatefulWidget> on State<W> {
 
   /// Hook fired after each successful page merge. Default: no-op.
   /// Override for image prefetch, syncing a base-class `items` list, etc.
-  void onPageLoaded(int _, List<T> __) {}
+  void onPageLoaded(int _, List<T> _) {}
 
   /// Synchronously clear pagination state and bump the generation counter.
   /// Call from inside the subclass's `setState` before awaiting