Convert PNG to WebP

Whichever you ask for. Leave the quality at its default and you get lossy WebP, which is what you want for a photograph and gives the large savings. Take the quality to the top and the encoder writes lossless WebP instead, which is pixel-for-pixel identical to your PNG and still usually smaller than it. For a screenshot of an interface or a diagram with text in it, lossless is the honest choice; the text is exactly where JPG-style compression looks worst.

Lossless WebP takes roughly a quarter off a typical PNG, which is real but not dramatic. The dramatic case is a PNG that should never have been one: a photograph with a transparent background, exported at full size, going from four megabytes to two hundred kilobytes as lossy WebP. If your PNG is a small icon or a simple diagram, expect a modest saving and consider whether the change is worth managing two formats.

Yes, fully, in both modes. WebP stores an alpha channel exactly as PNG does, with the same 256 levels, so a soft drop shadow or an anti-aliased edge comes across intact. This is what separates it from JPG, which is otherwise the obvious way to make a photograph smaller and cannot hold transparency at all. It is the main reason WebP replaced PNG on the web rather than sitting alongside it.

For a public web page, just WebP is fine now. The browsers that cannot read one are far rarer than the browsers that cannot run the JavaScript on the same page. Serving both through a picture element is still worth doing if your audience includes people on locked-down corporate machines with very old browsers, or if the images are also downloaded and opened in desktop software, where support is genuinely patchier than on the web.