That's how it works.
The browser has two filesystem APIs. The older one just lets it display a file chooser, and then the browser gives it access to that one file that the user picked, sandboxed, and nothing else. Any writes are cached until all security checks are passed, and then the browser copies the data out of the sandbox.
The problem with that is performance. So there is a second API which creates an isolated, sandboxed, quota enforced filesystem just for that one website. The quota counts for everything the site stores, including cookies and other stuff. It gets cleared when th user clears site data, e.g. automatically on closing the browser. The benefit is performance for cached data.
I know you hate it, but a lot of people use web apps. Office apps, CAD apps, games, IDEs, all sorts of things. I'm sure one of the reasons why Linux has been able to make gains lately is because so many popular apps only require a web browser now, not a compatible OS.