GIFs on X are actually silent videos
This is the most confusing part. What loops on your timeline as a 'GIF' is stored by the platform as a silent MP4 — real GIF files are far too heavy, and the platform stopped using them years ago. So what you download is a .mp4, not a .gif. If you genuinely need the GIF container, convert it after downloading; but if you're reposting it anywhere, uploading the MP4 gives you a sharper picture at a smaller size.