Thats on android only. And no, it isnt. If its a PWA then that button changes to “Install”. Which does almost the same thing as “Add to home screen” except it opens the webpage up as if it was a separate app. That means it gets its own entry in the “Recent apps” list and its own icon, and it hides the address bar.

Edit: You can test this yourself by going to lemmy.world on your phone. It is a PWA. Any website can really be a PWA, it just needs a manifest file. Lemmy.worlds manifest are available here and you can see what settings it contains.