There was a File System API but shown as deprecated now:
https://developer.mozilla.org/en-US/docs/Web/API/Window/requestFileSystem
There is now another, File System Access API:
https://developer.mozilla.org/en-US/docs/Web/API/File_System_Access_API
What happened to the old API and why was it discontinued? Should the new File System Access API be stable in all common browsers?
It turned out that File System Access API is not deprecated, it's just not standardised (May 2021); the deprecated one is the function window.requestFileSystem; the same function on Chromium-based browsers is window.webkitRequestFileSystem.
File System API is for creating a virtual drive (temporary or persistent) for each website when using browser-based db (IndexedDB) is not necessary especially for the purpose of storing files.
https://developer.mozilla.org/en-US/docs/Web/API/FileSystem
File System Access API is different, it is for accessing the real file system of the OS. This API is now standardised and available on Chromium-based browsers (May 2021). Firefox has not yet adapted this API.
https://developer.mozilla.org/en-US/docs/Web/API/File_System_Access_API
Status of these APIs: https://developer.mozilla.org/en-US/docs/Web/API