Update pages and components for new module paths

Repoints imports at the relocated lib/api and src/contexts modules,
and refreshes Layout + Login alongside the rest of the migration.

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

frontend/src/hooks/useBudget.ts

@@ -13,7 +13,7 @@ import {
   deleteRecurringItem as apiDeleteItem,
   upsertBalanceOverride,
   deleteBalanceOverride,
-} from '@/api';
+} from '@/lib/api';
 
 export function useBudget(initialYear: number) {
   const [year, setYear] = useState(initialYear);