Did you try any of the more common image editing software? Both MS Paint and macOS's Preview allow the common workflow of open → edit → save.
Affinity Designer isn't an image editor. Consistent with its name and marketing, it is graphic design software.
Obviously I have no objection to GIMP positioning itself as a graphic design program rather than an image manipulation program. However, if that's the direction they wanna go, perhaps they might consider changing their name to something other than "GNU Image Manipulation Program."
Both of your examples also do not have a native format, due to not having features making one necessary.
As a Mac user, I can't recall seeing this behavior anywhere, so I checked all the graphics programs I have here. Affinity Designer, Graphic (formerly iDraw), and Pixelmator all use "Save" to mean the application's native format, and "Export" for other formats. So do Apple's iWork apps. So do Omni's apps.
In fact, I can't find a single program that works the way you say "nearly every program in common use" does it. The Apple Human Interface Guidelines call for a Save/Export split along these lines, too, so it's not just a lone Adobe mistake.
Is that a Windows convention? The GNOME/Gtk+ community has not tended to follow Windows UI conventions.