Right-click, “Save image as…”, and the file ends in .webp. Many sites serve WebP because it loads quickly. Browsers and current phones open it, but older editors, some upload forms and a fair number of desktop apps still expect PNG or JPG.
Does the transparent background survive?
Yes. PNG has the same kind of alpha channel as WebP, so transparent and half-transparent pixels stay that way: a logo cut out on a website stays cut out. This is the main reason to pick PNG over JPG for a WebP. A JPG has no transparency, and the converter would fill those areas with white.
How much bigger will the PNG be?
Much bigger, if the WebP is a photo. A 38.0 KB WebP of a coffee cup (600×400) came out as a 480 KB PNG, about 12 times larger. A 1000×872 picture of the Hubble Deep Field went from 135 KB to 1.9 MB. Both WebPs were saved with lossy compression, and PNG has to store the result pixel for pixel, grain and all.
For photos, that size buys you nothing. The same coffee cup through WebP to JPG was 48.3 KB. Pick PNG for logos, icons, screenshots and anything with sharp text or transparency, where PNG stays small and JPG would blur the edges.
What happens to an animated WebP?
You get a PNG of the first frame. The converter does not create animated PNGs.
Anything else that does not carry over?
EXIF details such as the camera or date, if the WebP had them. If it carried a rotation flag, the rotation is applied to the pixels and the PNG comes out upright.
Need a transparent background that the WebP never had? That is a job for Remove background.