Blender 3 Pose library Sept 2021 update
This is a quick update for Blender 3 - Pose library (Sept 2021). Now you need to activate it as an addon in Blender 3 alpha.
The asset library editor window is now included by default.
You can also try to go to Edit - User preference - interface - display - developer's extra (mark the checkbox) and a new EXPERIMENTAL category will open in the left side menu of the user preferences.
Activate it, and find "Asset Library" to test storing your assets, by going to the outliner, right click - "Mark as asset" (for now it works for materials and models). The "Animation" category will store your POSES, but there are plans to implement storing animations in the future.