Tap Pants, shorts, french knickers, big loose bottoms are very much A Thing here. But something we get asked all the time is "won't those show up under clothes?"
Just because something involves more fabric than contemporary briefs doesn't make them more visible.
They're made from lightweight fabrics, and they compress under clothes. Buttons can be the part that are most likely to show up, but they tend to go down the side. The ones I'm wearing in the video are Harlow and Fox's extremely delicious silk ones, but if you're on a budget then both the Bettie Page range and the Fuller Figure Fuller Bust x Playful Promises feature some poly satin ones.
You can also find more contemporary versions with no buttons, such as these from Emma Harris.
If you wear a dress made from very fine fabric (perhaps with a lot of stretch) then you may find some aspects of your lingerie show through - but most clothes of any quality will cover up the delicate fabrics and fittings used in underwear.