You just want to use it on the web? Just so that. You get the full experience because there is no resource split between the web site and native apps.
You want to find the app in your favourite app store? It's there. Just install it.
You like the web version but want to add a shortcut to your app list? You can do that and there is enough metadata available to provide nice icons and titles.
Unless you are an owner worried about PWAs being normalized so that your tracker infested app stands out.
It won't be a "full experience". It's amazing to me that people are talking about GUI apps and keep pretending that GUI-wise the web is anywhere on the same level as anything native. I wonder why the https://open-ui.org effort exists if that is the case (because it isn't, of course).
And those almost invariably suck. A few try and invest in smooth-enough experience because customer retention affects their bottom line (e.g. Foodora is a suprisingly nice app), but those are not enough to say "You get the full experience".