Had a bit of a mental trying to do the UI Gymnastics for Pose Libraries
Wasted a bunch of time and wished there was something this simple to get me started:
To create poses from different models and store them for your Asset Browser:
1: Select all bones you want to be saved as a pose
2: In the Dope Sheet or Timeline right sidebar (n key), click Copy Pose as Asset.
3: In the file you want the poses to be stored in, In the Asset Browser,
set the Library to Current File and from the Asset menu, click Paste as New Asset
4: Create a folder in Asset Browser(+ icon under the library selector dropdown) for poses to organise them better,
otherwise they’ll be found in Unassigned
5: Double Clicking a pose from the Asset Browser will apply it to only the bones selected while in pose mode,
and like as if it was a ShapeKey with a Strength of 1
6: Single Clicking from the Asset Shelf (Only present in Pose Mode, Viewport sidebar > Animation > Toggle Asset Shelf) ,
will also give a Blend Factor slider that you can use to blend between the current pose and the applied one
7: Poses won’t get keyframed when you apply them, so rember to key the bones you want to be set,
or have autokey on when you apply the pose to get everything keyed
Sanity saved.
If you re-open your Pose Library file and don't see the poses in the asset browser, but they are present in the Asset Shelf,
Check that the Asset Browser is set to the Current File and in the right folder
Poses will probably have issues with some bones if the scales are different between the rigs.
(Good luck getting poses to fit otherwise)