Pinned Tabs (or App Tabs) allow you to keep your favorite web apps, like Facebook and Gmail, open and just a click away. This article explains how to use them.
On mobile I'd like to make paypal a pwa but it doesn't support it. I'm not aware of a mobile site that has pwa support that I'd like to use. (My fault or the website's fault, not firefox)
On desktop there is no pwa support. I just found an extension for ff https://github.com/filips123/PWAsForFirefox but it doesn't support flatpaks, hence I have to install firefox in a distrobox, I'll check it out
What do you meant doesn't support it? You can add any site to your home screen on mobile.
But yeah, having some sort of PWA mode would be cool. I remember Firefox used to have something like this but they killed it. Then PWAs became "cool". I think it was called Prism or something.
I don't think you quite understand how PWAs work. "PWA" doesn't really mean anything. It is just the idea of a website that behaves like people expect of a native app. Offline support is generally accomplished via the Service Worker API which Firefox fully supports. I have offline "PWA"s on my home screen right now. But these APIs don't actually depend on anything about the home screen. Even just navigating to an offline-capable "PWA" via URL should just work in Firefox.
Maybe some sites special case Chrome, but that is a limitation of the site, not any limitation of Firefox.
One collary as that with an ever growing set of APIs associated with PWA there is going to be some features that differ between browsers. For example Firefox currently doesn't support receiving shares but Chrome does. But I can't think of any "fundamental" PWA API that Firefox on Android doesn't support.