what are .webp files and why has my online experience been plagued by them?
I don't know what a .webp file is but I don't like it. They're like a filthy prank version of the image/gif you're looking for. They make you jump through all these hoops to find the original versions of the files that you can actually do anything with.
Edit: honestly I assumed it had something to do with Google protecting themselves from image piracy shit
Webp is a fairly standard if rather new image format, that are frequently used by websites due to their small file size. To further cut bandwidth costs and loading time, websites will often only include a tiny webp of an image until you click to expand or something like that, so that they don't have to serve a massive image if the user will only even see a thumbnail sized preview. However, this does break the "save image" button as if you try to download the thumbnail, say from google images.
Completely separately, some scummy sites will make you sign up for an account or something to download a full size image, and the only advice I have here is that it is almost always faster to find another site with the image then jump though the hoops.