Yes, if the game detects a supported controller, there should be a prompt screen to select the input before getting to the main menu.
Other games detect and work with those. DOS2 seems to detect them only on previously mentioned game type choosing screen.
Does the Classic version detect the controllers?
Only as mentioned.
Try right clicking the '..\Divinity Original Sin 2\DefEd\bin\EoCApp.exe' executable file, select Properties, switch to the Compatibility tab, and check off the option to always run as administrator, to see if that helps.
Admin / no admin no difference.
Try switching the game windowed or fake fullscreen display mode, to see if that will make a difference.
No luck.
Have I missed something in x360ce_x64 ?