A photographic PNG can be worth testing as WebP for a website. It may be a camera image exported from a design tool, a rendered room scene or a flattened promotional graphic. Make a separate export and compare it with the original rather than deleting the PNG immediately. File size depends on the image, so the useful saving is the one you actually measure.
Transparency needs special care here. Although the WebP format can store alpha, this tool currently renders WebP output on a white background. A transparent input will therefore lose that transparent area in the export. Keep PNG for logos, cutouts and overlays that need to sit on different backgrounds, and use this conversion for images where an opaque result is appropriate.