What will happen when Chrome drops the Cookie?

Google announced early this year that Chrome is seeking to roll out its Privacy Sandbox by the year 2022, which has caused quite an uproar in the online advertising community.  The reason: this project will drop support of third-party cookies, which as we know are used extensively in digital marketing for click attribution, conversion tracking, and more.  Google obviously stands to benefit from this, as advertisers will need to use Chrome's native toolset.  However, I'm curious about whether this will lead to the demise of the HTTP Cookie as quickly as many believe.

According to Statista data, Chrome currently leads market share for internet browsers worldwide, accounting for about 65% of the market:

This is likely due to the overwhelming prevalence of Android phones worldwide as compared to iPhone, whose default mobile browser, Safari, comes in second place.  My question, though, is what Apple & other browser developers' response will be to this announcement.  The nice thing about the HTTP Cookie is its transferability across all browsers; each implemented Cookie support, and so ad developers needed only to worry about a single protocol going forward.  Google may be developing a more secure and privacy-focused solution to replace the Cookie on Chrome, but will Apple do the same for Safari, or Mozilla for Firefox?  And if so, what will the implementation look like; will it be common across all platforms?

We have some time to see how this plays out, with two years still to go before the Privacy Sandbox is released, but one thing is for sure: the world of user tracking across various mobile and desktop browsers is in for a big shake-up.