Using the plugin linked below, I see it offers a setting labeled "Enable Server-side Auto Skip". I assume this makes it work with alternative clients like Kodi.

It is literally called Intro Skipper and it requires the Media Segments API as well, if memory serves, because you can do some customization to help define the intro and outro that isn’t auto-recognized.

E.g., I created my own Mass Effect “show” that I loaded into my Jellyfin, and I don’t have a true “outro” for my episodes, so it just defaults to “Next Episode” with 30 seconds left. But I did create a specific intro for the “show”, and without it being a legit TV show, the intro automatically picked up the intro across the episodes and gives me an option to skip.

I can’t speak to Kodi, but you can check the project on GitHub: https://github.com/intro-skipper/intro-skipper