We built Homecrew to solve it for us and open-sourced it. We use it to share skills, make them accessible to every agents, and keep everything in sync.
It works for managing and finding skills outside of your team as well, but its primary motivation was sharing private internal skills.
It's git-based, so if your team has a git repo of skills, Homecrew should "just work".
Hope you find it helpful. Would love any feedback.