TL;DR this just moves the search query data from URL to local state and removes query from title.

You gain better privacy because no search data will be sent to hosting service or saved in browser since the search query lives in state and not in a URL parameter.

Drawback is slightly worse user experience, since no data is saved in the URL you will lose your search on refresh.

For complete privacy you should also setup your own SearXNG instance since the search data is still sent to the default one, full guide here.