The Switch does have a usable web browser, it's just difficult to access. The eShop and some online features run on it, but it can be accessed and used as a standalone browser.
Sorry, I should have said user-exposed/user-visible (and I've edited). It's the same situation with the PS5.
Clearly, Nintendo doesn't consider it good enough for general use. And having played with it, I very much agree—it doesn't work on lots of sites and likes to crash a lot. I assume the PS5's browser is the same.
I'd certainly agree there. The eShop applet runs on it, and is easily the worst-performing part of the Switch - much slower and laggier than pretty much any site on the modern web.
https://switchbrew.org/wiki/Internet_Browser