I think a good rule of thumb is: am I mostly clicking or mostly scrolling? If I'm mostly clicking - say, something like AirBnB or Zillow or Discord - where I'm exploring things and interacting a bunch, that feels better to me as a rich client-side application. If I'm mostly scrolling, like a blog or substack or a newspaper or even twitter, that feels better as a website.
I thought of a good concrete comparison: Vanguard vs. Coinbase Pro. Vanguard is a website, and it basically works for them because their business model is very passive, but you wouldn't want to do active trading there. Coinbase Pro is a web application where you can do lots of exploration and take actions quickly, and for me, it would be a major hindrance if they implemented it in a traditional page-based way.
It's sad how many "web apps" (and even more regular sites) only work in Chrome - try using Firefox or any non major browser, and quite a lot of the web simply doesn't work.