You realize the app recommended is the Guardian’s and uses updating notifications to present in a predictable manner and context? This seems like an improvement in user experience over keeping this in a tab along all the other tabs and having to meander past your regular distractions, many of which might present results in a less restrained manner than what is being advocated for here. It seems like you saw the word app, made a throwaway, and ranted about the word app.

I was surprised how many different permissions they wanted for a news app.

Also, does Apple list permissions? I couldn't find it on their website (easily). I did find Google play store permissions easily.

It doesn't. You can just use the Google widget for it - https://www.google.com/search?&q=us+election+results

Are webpages allowed to edit the contents of already-sent notifications?

Most of the large newspapers and media sites will have this.

A live updating page with the results as they come in, and often with their predictions once they are able to call the results.

Just pick whichever media site you like best.

It's really your phone manufacturer's fault for giving apps a higher status than web-pages.