Third-party (AKA cross-site) cookies are harmful to the web, and must be removed from the web platform. This finding explains why they must be removed, and examines the challenges in removing them. We highlight some use cases that depend on third-party cookies and offer some examples of designed-for-purpose technologies that can replace them. Specification authors are expected to ensure they do not undermine the benefits of removing third-party cookies when proposing new web platform technologies.
Mozilla has already shipped strict privacy mode by default in recent versions of Firefox so they’re already a leg up on this.
Google is currently trying to transition people to its own proprietary method of tracking (where the browser itself tracks you) so they would love it if third party cookies were no longer usable for that.
Mozilla has also added a direct tracking feature (anonimized) to Firefox btw. Not sure what their agenda is.
Websites are irrelevant, if third party cookies stop working in major browsers there’s no point in setting them anymore, they’ll be ignored.