Are there any browsers which allow you to do your own electron-like wrapping of webapps? Would be nice to have your own native icon etc, but also be able to tune exactly what behaviour you want, for instance set per app caching levels, cookies, what happens when it goes to background, etc.

A good example is on mobile, where playing media on the web is a hassle because you never know what the background behaviour will be, whether it’ll carry on playing when you’re on another tab, or on another app, or with the screen off, or after five minutes. It seems to be a free for all now for the browsers, not much user control.