To me what cameras support as an output is irrelevant. On a pro camera you generally use the raw files as a default format. What is important is the formats you can export to / manipulate afterwards for publication/exchange.

Always always always -- and it's often multiple problems, where the filesystem preview generators don't support it or don't support it over a network or the social media used by the other person doesn't support it (often egregiously so, where an unrecognized drop bubbles up to browser scope and blasts the page you were on) or there's a weird problem with a site/app that is supposed to support it, such as it turns into a black box.

Support for webp is still so rough that I have to wonder what one's ecosystem must look like for it to be seamless. Maybe if you are a googler and your phone/computer/browser use entirely google software and ditto for your friends and your friends friends and your spouses? Maybe?