In absolutely all cases, if you see an animation on an artist’s twitter you should check if they have it available on any other site they use; it’s practically guaranteed to be better. If nothing’s available, then you’re going to want to convert that proprietary aberration of a format into a gif or a webm.
Generally, you’re gonna want to convert to webm, as it’s a pretty straight forward conversion, accepts high frame rates and large palettes, and obviously audio. For that, go here: https://video.online-convert.com/convert/mp4-to-webm
If you’re sure the original animation was a gif or just want a gif that can play anywhere, then use the following to reconvert it back to a gif: https://ezgif.com/video-to-gif
In both cases, you can paste in the twitter post link into the URL field and that’s it. For gifs you may want to try some further optimization.
Anyway, stop using Twitter, it’s terrible for all sorts of reasons, many far more important than it’s objectively awful UX or the crimes it commits upon images.