Where PS came from
PostScript is the page-description language Adobe shipped in 1984 with the Apple LaserWriter, and it effectively created desktop publishing. It is a full programming language that describes a printed page, executed by the printer's own interpreter. PDF is its modern descendant, but PostScript remains alive in commercial print queues, CUPS pipelines and Ghostscript workflows.
The technical picture
Compression: PostScript program text. Transparency: Not supported. Animation: Not supported. Colour: CMYK and spot colours. Typical file size relative to WebP: considerably larger than WebP.
Where it opens
PostScript printers and RIP systems. This is usually the deciding factor when choosing between PS and WebP — WebP renders in every browser but is uneven in desktop software, while PS has a very different support profile.
Converting PS to WebP
PostScript files need an interpreter to view. Rendering to WebP gives you an image anything can display. The output is a raster image in a PostScript wrapper, not vector artwork.
Converting WebP to PS
Commercial print services, prepress systems and Unix CUPS queues sometimes require PostScript input specifically. This wraps the image in a PS envelope those pipelines can rasterise. Expect the PS output to be considerably larger than WebP — that difference is the price of getting a format the destination will actually accept.