I found the error origin:
There are no missing files or connections in the .unit or .unit_skin. (I crosschecked the file structure with other base-game ships, and my modded ships work fine inside the game as well.)
However, SolarForge is unable to find the .unit_skin file (or any other file referenced in .unit) if it is not located in the base-game folder ("D:\Steam\steamapps\common\Sins2" in my case). I copied the .unit_skin from my mod folder over into the "...\entities" folder from the base-game and the error chenaged to "weapon_definition not found".
So the .unit_skin can now be found, but the next reference, the weapons, not, which is fine because I know I only copied the unit_skin over, not the weapons.
Conclusion:
Editing via SolarForge is not possible because I am working in a separate folder from the base-game?