The pyodide project managed to allow mounting the file system access API as a FS backend:
https://github.com/pyodide/pyodide/blob/eae76c367abdf42953065bfec86c66c3d4b82b2c/src/js/api.ts#L545
It would be great to include the native file system in addition to the other supported file systems (MEMFS, IDBFS, NODEFS).