Not OP, but I'd start with a one-click way to "install" the PWA apps using an API, e.g. with a banner (like on Android) instead of an item in the share menu.
Oh God, this is one of the reasons people hate PWAs. No more banners on websites! I don’t want to see sites even more cluttered.
Probably background services and processing, something even native apps can’t do.
More low-level camera access would be a nice improvement. Also, the ability to work with raw video data for trimming/editing.