Since I'm not a Civil 3d user I did not test my Open With solution.
But looking at your screenshots of the registry and reading up on how Civil 3d is launched I think I see the issue.
Since Civil 3d uses the same acad.exe as vanilla AutoCAD but with specific switches, there's no way to distinguish the two under the Open With menu:
https://www.autodesk.com/support/technical/article/caas/sfdcarticles/sfdcarticles/How-to-distinguish...
Another solution though not as good is to add program shortcuts into Explorer's Send to menu.
To customize the Windows "Send to" menu, press Winkey + R, type shell:sendto
and hit Enter to open the folder containing the SendTo menu shortcuts
Next open another Explorer pointed to this location:
C:\ProgramData\Microsoft\Windows\Start Menu\Programs
Look under Civil 3d as well as vanilla AutoCAD folders for their respective shortcuts and copy+paste to the SendTo folder location.
Now when you right mouse click on a dwg and select Send to you should see different AutoCAD shortcuts to open.
The drawback with this is that it will launch a new session of AutoCAD and not use a currently opened session.
