DE is not very effective with flying bugs. DE has to be dry to kill them. The bugs have to physically come into contact with it for it to kill them. Putting it on top of a substrate amounts to a muddy mess that allows very little water through, which means it'll take 30mins to water 1 pot properly.
Encircling your grow area with some DE can help stop anything that crawls over it, but again.. it's a fucking mess and horrible for fan motors and such. you'll kill a duct fan if you keep spritzing that shit around. Don't vacuum it up unless you want to throw out that vacuum. it puffs up in a cloud very easily, so it's going to slowly ruin any motor that is exposed to it. Your lungs aren't fans of it either.
I'd wager 1M USD on a bet taht DE vs bti with an ongoing infestation, because it is a foregone conclusion. 99-100% of the infestation would be gone within 1 life cycle or about 3 weeks with Bti. DE isn't even going too put a noticeable dent in the population in 3 weeks.
Side bet -- 1 Sticky trap would catch more adult gnats than any amount of DE strewn around your floor or on your pots.. making a fucking mess and doing very little.
FWIW, neither a sticky traps or de is going to be effective against an infestation nor stop one from escalating. A sticky trap will however speed up the process. Really isn't rocket science to see why it helps, Bti prevents larvea from surviving and traps kill adults thet already matured before you put bti down. Otherwise you have to wait for the adult gnats to naturally die.. why add a week or 2 when you don't have to?