Why do pictures I save from websites come out as WebP?
Sites send WebP to browsers that show it, to save bandwidth, and Save image as keeps the file the browser received. Converting here gives the JPG an older program or an upload form expects.
Why is my JPG bigger than the WebP?
WebP compresses better, so the same picture needs more bytes as a JPG to look the same. Lower the quality a little, or set a size limit, if the JPG must stay small.
Can I convert WebP to PNG instead?
Yes, pick PNG under Save as. A PNG keeps the transparency and loses nothing more, at the cost of a larger file; JPG is the smaller choice for photos.