"Writing a browser" (from scratch) at this point basically means you are implementing a type of portable operating-system-in-a-box (the web platform) and that it will be compatible with whatever Google decides to add to theirs. The browser is so comprehensive in functionality and APIs, and such a challenge to keep up with Google's constant churn of new features and total dominance, that not even Microsoft could do it…
Not really. If you limit your scope by saying that you're building a hypertext document viewer, it suddenly becomes approachable. A lot of the functionality is all that PWA stuff no one asked for and no one is using for anything good anyway.
WebSQL? IndexedDB? Service workers? WebGL? WebGPU? WebBluetooth? WebRTC? Just act like it all doesn't exist. 99% of actual websites — not web "apps" — would not lose any functionality.