There’s quite a bit of info on the forums for air-cooled/water-cooled spindles with VFD’s. Here’s one link: VFD and Air cooled spindle
If you search for “VFD spindle”, you’ll find several posts about them.
I have a 800W air cooled spindle with a 2.2KW vfd, and I love it. You don’t have to worry about a water cooling system, and it’s quieter than the Dewalt setup.