Google aren't pushing WebP. Google Docs / Slides still don't support it.
I appreciate Google isn't a monolith, but that lack of consistency makes it really hard to shake the impression certain tribes within it are at war with each other.
This is actually a good counter argument for 'Google is pushing X'. If they were pushing X, they'd make all their apps fall in line.
Contrast this to, say, Apple - which when decides to push something, they go all in. And that's an example of top-down decision making.
It's not war, it's indifference. Why should Docs give a damn what Chrome's priorities are? The only reason they would is if there were effective leadership ensuring company-wide alignment, but there is no one filling that function.