I genuinely didn't even notice the first time I downloaded and viewed a .webp. Firefox and Gwenview (the KDE image viewer) handled it just fine. So does GIMP if I want to edit one.
What common software are people trying to use that doesn't support it?
I have no idea. I had a funny issue where .webps had a different default program, but that was the only time I've had to think about an image extension (I use Linux too (Mint btw)).