Convert WebP to PNG
The right conversion when the WebP has transparency you need to keep — a logo, a cut-out, a sticker. PNG holds the alpha channel that JPG would throw away, and everything opens it.
Questions
PNG or JPG for a WebP I saved from the web?
PNG if it has transparency or hard-edged graphics and text; JPG if it is a picture and you care more about file size. PNG is lossless, so it will usually be the larger of the two for pictures.
Does the transparency survive?
Yes — PNG has the same alpha channel WebP does, so nothing is filled in and nothing is flattened.