Try exiting out of Galaxy, and starting the launcher from the '..\Divinity Original Sin 2\bin\SupportTool.exe' executable. The SupportTool.exe programs in the folders with the EoCApp.exe executables will just start the respective version of the game (and monitor for crashes, popping up a crash report window if the game does crash).

If the launcher doesn't start at all, try reinstalling .Net Framework 4.

If that doesn't help, try deleting the config.xml file in the '..\Divinity Original Sin 2\bin' folder, as well as 'C:\Users\<UserName>\AppData\Local\LarianLauncher' (copy and paste %LocalAppData%\LarianLauncher into Windows Explorer to quickly open that folder).
After that, try verifying local files again.

If that doesn't at least get the launcher starting from the executable, there is also a Microsoft .NET Framework Repair Tool, or if that doesn't help, Cleanup Tool.