Could be helpful to maybe use data from there. But there is a catch! The is no offical license seen for map data. Furthermore the map is using Google map for base.
If Läänemaa gives permission to use the map data for OSM but the map has Google base map, would that still violate OSM TOS about using proprietary map data?
If the owner of the website provides compatible license or explicit permission, then it doesn’t matter what basemap it uses. You could even use the .json files directly the get the POIs. For example, here are the cafe/restaurant data from https://laanerada.ee/wp-admin/admin-ajax.php?action=get_object_set&category_set%5B%5D=250&category_set%5B%5D=235