I'm using a web app to distribute my free software instead of the app store. I simply didn't want to join the developer program or go through the approval process, not to mention learning how to code in another language. But even more important, the exact same app can run on MacOS, iOS, Windows, Android - or any hardware/platform that has a browser.
A web app is basically a website with additional resources that allow installation on the device where it runs independently in its own window using the browser engine but
without the browser user interface. But it can be accessed as a regular website without installation too. On MacOS, Safari pretty much stands alone in
not supporting web apps while all the other browsers (Chrome, Edge, Firefox, Opera, etc) do. But web apps
are supported in Safari on iOS, although Apple does its best to conceal this fact. Go figure!
There was a
front page article about web apps recently. They can be very powerful, but also have some strict limitations to help prevent them from doing anything malicious. They really have no access to the device filesystem, aside from opening files that the user always has to choose in a browser dialog or exporting data to your downloads folder. They would not be capable of the "window management" that the OP is interested in either.