Keep search snappy with useDeferredValue

## Goal
Use `useDeferredValue` on the search query so typing stays responsive even with an artificially expanded list or intentionally heavy filter.

## Acceptance criteria
- [ ] `useDeferredValue` wraps the search query value
- [ ] Filtering uses the deferred value
- [ ] List is large enough (or filter heavy enough) to demonstrate the difference
- [ ] Optional visual cue when results are stale

Start by locating the search query and its filtering logic, then run the app with the current search behavior. Apply the acceptance criteria around deferred filtering and a sufficiently large or costly result set; verify that typing stays responsive and check whether a stale-results cue is useful.

Written by the indexing model from the issue text.