Flatpak is probably the worst way to "have" this possible. It's completely opaque to both app and user. If you ever tried to run an .exe through flatpak'd bottles, you'll run into an issue where .dll's aren't found because you didn't install flatseal first to configure permissions. That's not operating-system level integration. That is actually very poor design that a user requires a separate app (flatseal) to configure how the sandbox works.

I was thinking about desktop OS's, actually.

You don't need to use that Windows API. You can just access any file you want. There is no reason a music player, for example, needs to access ~/Pictures. An arbitrary program requiring access to all your files is a huge red flag, but it's a red flag that users aren't allowed to see. Proper filesystem permissions would fix that.

That just means it's poorly designed. There has to be a way to design this in such way it works.

That does not sound at all reassuring, that the only safeguard is the system blocking access and that the API has no safeguard.

Its also easily possible to have sensitive files misplaced, especially for a general non-technical user that would be the one falling for a browser hijacking attack

i give zero F about whatever is in my /usr, /var/lib and /opt folders.

what are websites gonna steal, debian binaries and libraries?

all my important stuff are in my home directory, which is owned (read+write) by me, the same user running the browser.