WHAT DO YOU RECOMMEND
I would recommend the option to use GIFs as an Icon for a page.
HOW COULD IT BE DONE
This option is already given for the cover of a page (only if you drag&drop the GIF into the field).
Thus I came to the conclusion that the implementation is basically there already but the drag&drop field is just missing for this to work?
REAL WORLD USE CASES
For better personalisation one could add a GIF on a page to give it more life, just like with the cover of a page.
I know that you are asking specifically for GIFs but, you can use animated PNG as a replacement for GIFs and those work just fine (doesn’t work on Mobile, though).
You can check this How To to have an idea of the result.
Oh, I actually saw your post already.
The problem for me is that I am not trying to use an animated emoji but just some GIF I want to use as an icon.
If you know how to convert a GIF to an APNG, I would be glad to know! I saw some rather sketchy and long loading website just a second ago, but that lead to nothing…

You can download the PNG below, I downloaded your GIF and converted it using
freeconvert.com

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oh lol, I actually did not see that they have that tool.
when i searched for it online I just found that weird “ezgif” site and ye idk.
Thanks for telling me the converter you found 
That it doesnt work on mobile makes me still prefer having GIF support for icons, but APNGs still appreciated
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