I keep my wild Smarigdina in a 2.5g bare-bottom tank. His Hagen Elite mini filter (set on low) has a little added foam, but not much. And just a few Anubias, so no real plant help. I vacuum and change 50% once a week (easy to keep a bare-bottom clean). I get 0.00ppm ammonia and nitrite and ~5.0ppm nitrate every week. One drop/gal Prime with the change just to chelate the heavy metals (My well has no chlorine nor ammonia).
I would say that any sponge filter, even a small one, is plenty for just a Betta. When I activate my 3.0gals, I run an ATI Mini sponge filter, which is way overkill.