Here's my take:
Chrome, Safari, Firefox, and Edge all support WebAssembly today. It shouldn't be too long before we see native DOM support in WebAssembly, as well as some rudimentary implementations of UI abstractions on top of that.
I think within a few years, we'll see PWAs being written in various languages -- whether you're a classic JS developer or a hipster with a Go fetish -- and compiled to WebAssembly. PWA functionality is finally starting to be supported by Apple (mind you, it's terrible in iOS 11.3, but it's a start) which is great news. Web is still a questionable delivery mechanism for PWAs as they can be heavier (especially if people start compiling their own runtimes into their packages -- great opportunity for CDNs here I think!), but web delivery is just one way to do it. And it's not even that bad.
There won't be a separation between native and web: you'll have a project compiled to WebAssembly that is either delivered via the web, or via the Play Store/App Store/Windows Store. This is great news for devs and Microsoft (or any other company struggling in the mobile market because of the apps problem.)