Apparently this addon causes strange behaviour in blender 3.5 (and 3.6?).
If your blend file has multiple armatures, and you attempt to go pose mode, something happens to the addon and you'll be instantly kicked out of pose mode back into object mode, Disabling the addon fixes it, though I can suggest fixing this if it's possible.
I originally made report here : https://blender.stackexchange.com/questions/297283/cant-enter-edit-mode-when-i-have-multiple-armatures
And then someone had the same problem and found the cause : https://blender.stackexchange.com/questions/297328/when-i-try-to-go-to-edit-mode-or-pose-mode-of-an-armature-it-immediately-switch
Apparently this addon causes strange behaviour in blender 3.5 (and 3.6?).
If your blend file has multiple armatures, and you attempt to go pose mode, something happens to the addon and you'll be instantly kicked out of pose mode back into object mode, Disabling the addon fixes it, though I can suggest fixing this if it's possible.