Rotate origin only to match other object rotation

Question

import bpy, bmesh
from mathutils import Euler
import math
import mathutils

active = bpy.context.scene.objects['Suzanne']
obj = active.rotation_euler

for o_sel in bpy.context.selected_objects:
    selected = o_sel.rotation_euler

for o in bpy.context.selected_objects:
    
    if obj[-1] == selected[-1]:
        print('same angle')
        pass
    
    else:
        o.rotation_euler = (0, 0, obj[-1])
        mesh = bpy.context.object.data

        bpy.ops.object.editmode_toggle()

        bm = bmesh.from_edit_mesh(mesh)
        bmesh.ops.rotate(bm, verts=bm.verts, cent=(0.0, 0.0, 0.0), matrix=mathutils.Matrix.Rotation(-obj[-1], 4, 'Z'))
        bmesh.update_edit_mesh(mesh)
        bm.free()

        bpy.ops.object.editmode_toggle()

In Blender 2.93, let's say that I have one active object and I want all the selected objects rotate only their origin to match the rotation of the active one. After couple of hours I have faced a roadblock, where I can get the rotation of the active object only and then loop through the selected ones leaving the active out from the loop, but after that I can't find the way for the selected ones to rotate their origins only.

UPDATE: I manage to make it work somehow, if I select on object and ru the script, it will work as it should be, but if I have more than one object selected it doesn't work. I have tried different loops combination without avail. The second issue is if I replace the scene object for any active one, even the active will rotate which is not right.

UPDATE 2: Here is a gif showing the script in action and the problem when selecting multiple objects. As you can see, the monkey has the axis angle that I want the other objects to have, when selecting the Torus and run the script it works, the same goes when I select the Cube, but if I select both, the script is not working properly.

In the second video if I have an active object the selected ones will not rotate.

Answer 1

Match local axes.

Ok it appears you wish to match the local axes of selected to active object.

• The local X, Y, Z axes in global coordianates are the columns of the rotation part of the world matrix

   R = ob.matrix_world.to_3x3().normalized()
  

• Note Have not allowed for non uniform scale, so apply scale first. Could fix, was noticed after posting.

• Use the rotation part of the matrix world for all other objects. But keep there translation, this will align all local axes, but will noticeably rotate them.

• Transform each selected objects mesh by rotating back the local space equivalent of the global rotation. (mw here is the world matrix of the selected object)

   Rloc = mw.to_3x3().normalized().to_4x4().inverted() @ R
  

• Since the mesh is being transformed, ensure that each object has a unique mesh.

Test script. Run in object mode, changes local rotation of selected to active.

import bpy
from mathutils import Matrix
from bpy import context

ob = context.object
mw = ob.matrix_world
# rotational part
R = mw.to_3x3().normalized().to_4x4()

for o in context.selected_objects:
    if o is ob:
        continue
    mw = o.matrix_world
    Rloc = mw.to_3x3().normalized().to_4x4().inverted() @ R
    o.matrix_world = (
            Matrix.Translation(mw.translation) @
            R @
            Matrix.Diagonal(mw.to_scale()).to_4x4()
            )
            
    o.data.transform(Rloc.inverted())

Related How to properly use ExportHelper's 'axis_conversion' method? except using the active object as a basis.