It doesn't support "installing" PWAs like native apps, and that's a core feature of PWAs, so no it does not have great support for PWAs
> the name is horrible and damaging to Firefox so I'll probably not ship until that name is changed.
I think you're being a bit harsh here. Sure, a more accurate name would be "PWA Installer for Firefox", but to say it's deceptively named is pretty hyperbolic.
Is it different than Firefox's "Add to Home" button?
There are two ways to link to an application in Firefox: one just creates a shortcut ("Add to home") which opens the browser. The other opens a full screen application, like PWAs are designed to do.
When I hit the install button, what I really want is the latter but occasionally PWA detection seems to fail and installs a shortcut instead.
In desktop Firefox, Mozilla has decided to can this idea and not implement it. There was a bug open for this in bugzilla, but that was closed as WONTFIX.