There's better functionality coming, but for at the moment, users need to jump over to the apps domain to install. "Getting" or "Installing" means adding to home screen. The flow isn't ideal at the moment, and some web apps aren't installable (e.g. don't have a manifest/service worker), but it's early in the movement. You're not really missing anything, other than the fact that we have to start somewhere :-P

If you visit a PWA on Chrome for Android, you can install the app by tapping the three dots and scrolling down to 'Install app'.

OP has a filter for only installable apps, but it's off by default. So you might be taken to an app that's not installable.

We've been getting feedback to keep the "installable" filter on by default, which I think is a good idea. We'll implement tomorrow. Eventually this'll evolve quite a bit, but we're taking a measure approach. Stay tuned! :-)

It's the same for me, but I have already filtered for installable. I guess this doesn't work on desktop, Safari 16.1?

You'll need Safari 17 to be able to install (Apple calls it "add to dock"). Otherwise, try Chrome.

Yeah agreed - I thought it is a library of all these apps in one place which could be a cool thing. However otherwise it is just advertising for these apps listed