When I run yEd 3.19 with Java 11.0.2 on Windows 10 with a display resolution of 1920x1080 and display scale factor of 125%, label text in nodes and edges is actually scaled up as well.
Unfortunately, it is difficult to determine the cause for this problem without access to your system. What you can try to do, though, is resetting yEd to its factory defaults. To do that, quit yEd, delete yEd's profile directory, then start yEd again (see "Help" -> "About" for the profile directory location).
A word of warning: Deleting the profile directory will also delete user-defined palette sections and properties mapper configurations. If you have any of those, you can move the profile directory to another location instead of deleting it to be able to restore your previous settings in case deleting the profile directory does not help.