I tested this out on my own self-hosted site and see there are some UX issues here:
- After adding the custom user field, the new field did not appear in my user preferences until I refreshed the web browser. Same thing for user card and user profile.
- On the user list, the search field is descrbed as “filter by username” but you can search by custom user fields. That feels slightly strange to me.
Very prettily, the site search does work and indicates even which user field is a match:
Clicking a link to search from the user card or user profile does not exist for me. Is that a theme component you are using?