Most webdevs I know consider Safari to be the new IE - they often lag years behind implementing features that are key for new capabilities like WebAssembly multithreading - and it's not hard to see why - the web is a primary competitor to their App Store business.
On the other hand, I feel like the browser is almost done. With WebAssembly and WebGPU and a bunch of other stuff, I can think of very little in terms of capabilities that need to be added to browsers in the future.