Though I'm not a Pinterest user, my wife is, so I borrowed her account(!)
With hierarchical site structure and four main areas (home, discover, notifications, and account), the PWA is 100% familiar. Yes, it's the web, but it's more than that - it's faster, smoother and slicker.
Delving deep, here looking at Dr Who-themed creations in my wife's account. Yes, yes, you'd like a wife who likes Dr Who too. Sorry, this one's taken!
The notifications at work - they don't pop into the OS, at least not under Windows 10 Mobile, but then something from Pinterest is unlikely to be of high urgency, so it's not an issue.
Note also that there are a number of third party Pinterest UWP clients, including Piny and PinStar. None are dramatically different - this is Pinterest after all, so there's limited functionality (compared to, say, Facebook).
Pinterest's existence online as a PWA for mobile browsers is very welcome though - it means that you don't need a client or standalone application anymore. And if you want it on your Start screen, just 'pin it' in Edge. [See what I did there?!]