When I go to https://www.openstreetmap.org/search?query=54.93%2C13.38#map=4/54.93/13.38&layers=T, many country names are missing. Also missing are the names of bodies of water. I joined to fix this, but it appears that editing at this scale is not allowed. What can be done about this?
This is Public Transport map style. This, not the data, seems to be the issue.
See info: https://wiki.openstreetmap.org/wiki/Transport_Map about the authors.
If you accidentally changed from “Standard” style to “Public Transport” you can go back by clicking the Layers button on the right side of osm.org.
In most cases it is simply that, at that scale, there is not enough room to fit them in. In the case of Norway, there are two disjoint parts of the country and their renderer seems to pick https://www.openstreetmap.org/relation/5856703 as the place to plant the label, possibly because being far North, it looks bigger than it is.
In any case, there is a principle of not tagging for the renderer, so the only place to fix this behaviour is in the Transport Map’s render, not in the actual data.
Incidentally, it is possible to edit all this data (even with iD), but a newbie should not try to so, especially for well known country names. Either they will not have analysed the problem correctly, or the lack of the name will be the result of vandalism or a newbie edit and the data is likely to be reverted to its correct form, with all the detail, quite soon.
It seems that the only rendering that uses hint of the “label” role in the boundary relation is the humanitarian layer.