Notice This is from my own experience testing and making chatbots with gifs. Additionally for some reason this website does NOT support actual gifs. Instead they SUPPORT webp. Use https://ezgif.com/gif-to-webp , to convert videos or gifs to webp. And in theory should work when uploading the character background.

Also credit to u/Fool_Pricey for actually being the one who figure this out on the Yodayo Reddit discussion: https://www.reddit.com/r/YodayoAI/comments/19eegyt/how_do_you_make_gif_profile_on_tavern_bot_ive/