When I’m just at home, I wear the cotton tank tops with “shelf bras” (nothing more than another piece of the same t-shirt material with a bit of elastic at the bottom, so hardly a bra) from Duluth Trading. But I wear them inside out. That way, the cotton fabric is there to separate breast from torso and absorb any sweat, but the elastic band isn’t against my skin. Because the inside and outside fabric is the same, it just looks like you’re wearing a tank top with a band below the bust. Still, though, only for home. :)
If you want something to help when you’re out in a sundress or something, you can always apply a good antiperspirant (not just deodorant, actual antiperspirant) under your breasts. (It’ll block the sweat from forming, the same way it does under your arms.) I recommend Mitchum Clear Unscented Gel (or try the men’s version — exactly the same, but cheaper). If you’re concerned about residue, just apply it after showering the night before and wipe any excess off in the morning; they say it stops sweat for 48 hours. ❤️