I managed to use Natural Earth data to generate vector tiles, and serve it to the MapBox. I also use geoJSON data to show labels with country names.
Now, as you can see on these 2 animations - when zooming in the OpenLayers, labels have the same size, and no fade-in animation as it is the case in the MapBox example (among other things - formatting is also not in one line but in multiple lines etc.).
Is there any existing style for OL or some tutorial how to achieve this same effect?