My solution is to put them in a public GitHub repo and link the raw content URL.
Here’s an example:

- Image link: https://raw.githubusercontent.com/jbunke/tdsm-art/refs/heads/master/_tdsm/logo/itch/tdsm-itch-card-3-mini.gif
- Repository: jbunke/tdsm-art
This works for GIFs in project page and devlog bodies, but it doesn’t work for banners or background images, since those have to be uploaded via the theme editor.