The device does not read HTML index pages — it needs the directory listing as JSON. That is what autoindex_format json does. Plain HTTP only, so keep this on your LAN.

server {
    listen 8090;
    server_name _;

    root /srv/music;
    charset utf-8;
    sendfile on;

    location / {
        autoindex on;
        autoindex_format json;
    }
}

charset utf-8 matters for track names outside ASCII. Enter the address with the trailing slash: http://music-server:8090/