I have no plan for Wavekit at the moment. If you'd like to sponsor its addition to the add-on, you can send me a message with a list of the different kind of URLs that can be embedded and I'll get back to you with a quote shortly.
If you're trying to manually add the site for your own forums, you should look into a media site tutorial such as this one. It works well enough for simple sites with only one type of content (e.g. only playlists but no individual tracks) but if you need anything more elaborate, you'll need some PHP logic.
What URL did you post in XenForo to create this embed? What is the BBCode for this embed? What URL does that link take you to?
Also, if you look at your browser's error console, you'll probably see a message that indicates why it doesn't load Twitter. Chances are Twitter is blocked at the browser level or at the network level with a Pi-hole or something like that.