How does Flutter fit in with PWAs? From a high level they both seem to do the same thing: cross-platform mobile application platforms.
Dart has PWA support, see https://pub.dartlang.org/packages/pwa
PWAs will likely further rise in popularity and be very practical for good cross-platform support and ease of delivery - Flutter won't change that in the short term. In the long term, maybe it will.
There's no coherent view as to what they want mobile to be, just teams pushing their own things.
Flutter is trying to get modern concepts delivered without towing along antiquated/unneeded technology.
I'd personally be very happy with "compatibility" support of Flutter for the web, which seems to be quite easy (and performant) with wasm+opengl.