A GIF is an inefficient way to store video: converting one to MP4 routinely cuts the size by 90 percent or more while showing all the colours GIF had to throw away. Instagram and several other platforms do not accept GIF uploads at all but take MP4. The one thing an MP4 does not do by itself is loop; that depends on the player.
This is demanding work for a browser: a long or high-resolution file can take several minutes, and your device does all of it, so keep the tab open.
This pair uses the compatibility engine, ffmpeg built for the browser, because GIF is not handled by the browser's built-in codecs. It is a one-off download of about 10 MB that the browser keeps, it is slower than the built-in codecs, and it takes files up to 1 GB.