To answer my own question:
There isn't any specific "search" call. Just use the BackendService.getJSON() call. The BackendService is a thin wrapper for all API Endpoints.
Therefore for a basic user search it's simple backendService.getJson('/organization/query?q=johndoe&activeonly=true&details=true') with some rxjs in the mix.
The Query could be (safely) composed with Utils.buildUri() which is part of @eo-sdk/core.