No permission to write files to subfolders after granting permission to root or other folder of sd-card

In one step, I will be prompted to pick a folder at external SD card. I do and pick a folder.

    public void GetPermission(){
        Intent intent = new Intent(Intent.ACTION_OPEN_DOCUMENT_TREE);
        intent.putExtra("android.content.extra.SHOW_ADVANCED", true);
        startActivityForResult(intent, 42);
    }

    @Override
    public void onActivityResult(int requestCode, int resultCode, Intent resultData) {

        if (resultCode != RESULT_OK)
            return;
        Uri treeUri = resultData.getData();
        getContext().getContentResolver().takePersistableUriPermission(treeUri, Intent.FLAG_GRANT_READ_URI_PERMISSION | Intent.FLAG_GRANT_WRITE_URI_PERMISSION);
    }

later I download a zip-file (by asynctask) to picked folder from the Internet. Just to test I download the file to the picked folder with success through the following routine

        uri_ext = Uri.parse(uri_string);
        URLConnection conexion = url_download.openConnection();
        conexion.connect();
        int lenghtOfFile = conexion.getContentLength();
        InputStream input = new BufferedInputStream(url_download.openStream());
        OutputStream output = null;

        DocumentFile pickedDir = DocumentFile.fromTreeUri(the_context, uri_ext);
        DocumentFile newFile = pickedDir.createFile("application/zip", zipname);
        output = the_context.getContentResolver().openOutputStream(newFile.getUri());

        byte data[] = new byte[1024];
        long total = 0;

        while ((count = input.read(data)) != -1) {
            total += count;
            publishProgress((int) (total * 100 / lenghtOfFile));
            output.write(data, 0, count);
            if (isCancelled()) break;
        }
        output.flush();
        output.close();
        input.close();

after that the file exists in the picked folder. The download should not take place in the picked folder, but in a subfolder of the picked folder. So I create a subfolder with the following code:

        DocumentFile new_Dir = DocumentFile.fromTreeUri(context, uri_ext);
        new_Dir.createDirectory("new_subfolder");
        uri_string = uri_string + "%2Fnew_subfolder");
        // uri_string = uri_string + "/new_subfolder"); also checked
        // no other code, nothing else

after that the subfolder is present. Now I try to load the zip-file from the internet into the new subfolder with the exact same code (except for the uri path from varibale uri_string) from above. Result: the download to the new subfolder does not work.

Why? What am I doing wrong? What do I have to change?

After some tests I found an easy solution:

documentDirectory = DocumentFile.fromTreeUri(the_context, Uri.parse(path));
documentDirectory.createDirectory("new_subfolder");
documentDirectory = documentDirectory.findFile("new_subfolder");

after the last line it then continues with the above code and everything works. Maybe it was just too easy. :)