Quaternion mode?

[WeaselOnaStick]

This add-on seem to change many bones' rotation mode to euler which doesn't suit my needs at all. Plus, I think it breaks baking IK constraints entirely. I try to use blender's default pose bake and IK constraints just get deleted without impacting the bones

[Mwni]

You have to check 'Visual Keying' as stated in the docs for the constraints to get keyed.
The rotation mode does get set to euler I believe. That is simply because the effort was not worth it for me. But you can always adjust that bit of the code yourself. Replace the rotation_euler driver in drivers.py. bone_rot serves a rotation matrix which you can transform into the mode you want.

[WeaselOnaStick]

Visual keyeing is enabled. I tried both your operator and blender's default baking and neither really worked.

Sadly the code is a bit hard for me to edit. I would greatly appreciate if someone made a quaternion version of this add-on