Linux and Android handles .webp just fine tho, in windows try open source image viewer like imageglass and everything gonna work just fine, speaking from experience i had, just as most people here i hated that webp doesn't open until i understood that open source image viewers handle it just fine, then i liked that file format cause it's versatile i mean, it can be picture or animation like gif, and compression feels better
I can't speak for all distros and DEs, and I also don't do many image related things, but I'm using Linux Mint Cinnamon and the default desktop background manager doesn't support .webp. Sometimes I see a cool image that I want to use and I have to convert it; other times, when I notice it's .webp, I just give up on that image.