The "Pose Library" in Blender 2.93 LTS is ignoring bones with certain prefixes as described by Kent @theluthier in this lesson for Blender 2.67 and the "DEF" prefix :
This isn't explicitly mentioned in the "Pose Library" subchapters (see here and here) of the "Blender 2.93 Manual". We just read in the paragraph for the addition of a new pose:
Bones that are ignored by the Whole Character keying set are always ignored, regardless of their selection state.
The affected bone prefixes are mentioned here under "Whole Character Keying Set":
The built-in Whole Character keying set is made to keyframe all properties that are likely to get animated in a character rig. It is also implicitly used by the Pose Library system.
In order to determine which bones to add keys for, and which bones to skip, the keying set uses the bone names. The following bone name prefixes will be skipped:
“COR”, “DEF”, “GEO”, “MCH”, “ORG”, “VIS”