Before trying to extract and migrate the playlists from your old database through some SQL, it might be easier to actually re-do your migration (following the procedures to actually migrate your server instead of rebuilding it).
https://support.plex.tv/articles/201370363-move-an-install-to-another-system/
As for WebTools: I’m not sure, the old bundles will still be working with current releases of PMS. You can simply download the WebTools-NG app on your regular desktop, link it to your account and access the server from there (no need to install it on the same machine as your server). That being said… from what I’ve been reading, the newer versions appear to no longer support re-importing playlists (happy to be corrected).
