The main purpose of PWAs is not to remove the browser toolbar but rather cache most of the website to improve speed and reduce data usage if I am not wrong, there are external tools to get rid of the toolbar but Firefox dropped the PWA spec which includes a lot more than just that.
Seems like you are right, the caching for proper offline usage and use with very limited internet connections is all done trough service workers. Their main job seems to be system integration and while Firefox Android kind of sucks at that too it doesn't seem like they ever cut that down so they just dropped it for desktop users.
On Android at least, Firefox PWA's don't seem to support registering system-level things (like 'Share To' handlers) - you need to use a Chrome PWA for that....
Nice, I was trying to figure out how to get that working with Firefox. But, to be fair, it's not Firefox that's supporting PWA, it's the mint webapp-manager which is only included with Mint and requires extra steps to install on other OSes. Not as straight forward as PWA being directly supported by Firefox.