I’ve read your other thread. The UV data gets destroyed when you use dynotopo, but not if you are just displacing the vertex positions by sculpting with that off.
You are supposed to save texturing for after you are finished sculpting and modeling, but If you absolutely have to sculpt over a finished model, then you have to avoid using dynotopo or remeshing. If you need more geometry to sculpt on then you could try using the multires modifier. It can preserve the UV data because it adds geometry in a predictable way. The smoothing can alter the shape, so you’ll also want to click the drop down that says advanced then change the subdivision type to simple and UV smooth to sharp. It’s been a long time since I’ve tried to sculpt something, but at a glance it seems to preserve the UV data.