I encountered what I believe was the same problem you are describing. I believed the cause was some kind of bug in the migration of preferences from my previous SDDM 3.3 version. If I'm remembering correctly, it asks you if you want to migrate your preferences from a previous version during the initial startup of SDDM 4. I said yes the first time and was left with completely non-functional SDDM 4 after startup.
The solution I found was to remove the SDDM 4 preference directory and restart again saying, "No" to the preference migration. The preferences for me ( on a Mac ) are located under ~/.oraclesqldeveloperdatamodeler/system22.214.171.1246/.
Just now I've repeated this process, deleting the SDDM 4 preference directory, restart and say "Yes" to importing 3.3 preference. After startup, I'm again in a state where the application is unusable, I can't open a model, or create a new model.
Hope this helps.
I also faced this issue with Data Modeler 4.0EA2 (v126.96.36.1990) after accepting the settings migration of preferences from my previous DM v188.8.131.527 installation.
The solution to getting SDDM 4.0EA2 back to work was that Brian described: delete the preferences folder (on a Windows 7) C:\Users\username\AppData\Roaming\Oracle SQL Developer Data Modeler\system184.108.40.2060