feat(ST-507): show code badges on cards, lists and dialogs across the app

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

components/sprint/sprint-board-client.tsx

@@ -228,6 +228,7 @@ export function SprintBoardClient({
           selectedStoryId ? (
             <TaskList
               storyId={selectedStoryId}
+              storyCode={stories.find(s => s.id === selectedStoryId)?.code ?? null}
               sprintId={sprintId}
               productId={productId}
               tasks={selectedTasks}