Dithered 8-bit/256-color images will look 'better' than non-dithered 8-bit/265-color images, but it will almost always be worse that a 24-bit JPEG (no alpha) or 32-bit webP (includes alpha) and have a much larger file size.
I did some quick tests with https://squoosh.app. The 8-bit dithered PNG is >4x the size of the JPEG. It also shows some terrible banding on any kind of gradient in the image. The PNG is 5x larger than a better looking webP version of the same image.
I tested a lot of images (photos, drawings, digital artwork, etc) and some of the images were 10x larger as dithered PNGs vs webP/JPEG. Only one was smaller as a dithered PNG.