From my experience, it’s very rare to see someone not using Reaper for sound design. Some use Pro Tools or Cubase, but they aren’t as common as Reaper. It really has no competition due to how easy it is to prepare dozens of assets with a single render (all with correct naming and loudness) as well as extensions that add features no other DAW has (e.g. Global Sampler, stuff by LKC Tools, etc.).
It’s not very good for music, though, so here, the situation is a bit more diverse. So yes, I’m talking concretely about sound design.
I think now it seems clear you're talking about "sound effect design" specifically maybe, rather than sound design? Particularly because you say it's not good for music production, but plenty of us do sound design together with music product, but I've also never done sound effect design, which it does sound like you're talking about.