The first thing a web browser needs is a non-profit, propped up by an enormous endowment, so that they can stay independent in the face of unthinkable pressure and sabotage attempts from the tech monopolies.
The second is to enshrine one concept above all others: you are building a tool for the users. Not for yourself, and not for any company. Serve the users. Do not harm or exploit them.
The third is to understand that a web browser in the modern era is no longer a document viewer: it's a weapon of war. It must be assumed that every page you load is trying to do something nefarious to the user, from low grade like dark patterns and ads to high grade like phishing and full-on malware and hacking attempts. Start from a point of extreme skepticism. Nobody can be trusted, including (especially) not leading tech companies.
The fourth is to get rid of cancerous, masturbatory habits in programming like chasing after whatever language is most hip and stylish this week. Only three things matter: How efficient is the program, how secure is the program, and how quickly can you build it? These obviously pull in different directions, so a balance will have to be struck, but the point is there's no space for chasing languages or programming practices for vague ideological aspirations. Tried-and-true over shiny and new.
A new browser is definitely needed, and probably won't happen thanks to a near complete market capture by tech monopolies. But the solution to current issues isn't to make a browser that's even more drenched in them.
Edit: I will agree with the author on one thing though, which is that modern browsers do too goddamn much. Scale the shit back.