For the city of Bratislava, the only available ‘cities’ are the districts of the city, such as Relation: Bratislava - mestská časť Staré Mesto (1700677) | OpenStreetMap - level 9 on OSM.
I suggest adding the city in its entirety - Relation: Bratislava (1702499) | OpenStreetMap (level 7) and nesting the districts.
My profile link :murarzxvii - CityStrides
There seems to be the same issue with the city of Kosice:
we have the districts on level 9, such as: Relacja: Košice - mestská časť Barca (1698624) | OpenStreetMap
but not the city as a whole: Relacja: Koszyce (1690324) | OpenStreetMap
My suggestion would be to only add the city of Kosice as a whole and remove the districts, as it’s not as big as the cities that tend to have their districts available on the platform.