Its all part of the WP install; maybe more accurately, we would need a different search form for parent pages and their child pages, not a subdirectory.
So, for example, a search form on https://mindmgt.com/client-name/ that would only show results from its child pages:
https://mindmgt.com/client-name/sleep/
https://mindmgt.com/client-name/work/
https://mindmgt.com/client-name/
etc