Can't figure out local rotation axis.

Hello to all,
Here’s my setup: I have a cube which has 6 exterior faces which can be rotated individually along their Y (up) axis. Here are the cubes showcasing their pivot and local axis

The faces are rotated on Y axis with mouse drag with the following code:

Vector3 _mouseOffset = (Input.mousePosition - _mousePos);
Vector3 _rotation = Vector3.zero;
_rotation.y = (_mouseOffset.x + _mouseOffset.y) * rotationSpeedEditor;
                    
_selectedFace.transform.Rotate(_rotation, Space.Self);
                    
_mousePos = Input.mousePosition;

Now here’s the problem. Upon releasing the mouse, I want to smoothly rotate the face to the closest value between 0, 90, 180, 270 but assigning the localRotation I don’t get the desired effect because one face is rotating on the local Y axis and the other on the local X axis. Shouldn’t both of them be using the local Y for rotation?

Here’s the code I use upon releasing the mouse button

       Vector3 currentRotation =_selectedFace.transform.localRotation.eulerAngles;
        float currentRotationY = currentRotation.y;
        if(currentRotationY <= 45)
        {
            currentRotation.y = 0;
        }
        else if (currentRotationY <= 135)
        {
            currentRotation.y = 90;
        }else if (currentRotationY <= 225)
        {
            currentRotation.y = 180;
        }else if (currentRotationY <= 315)
        {
            currentRotation.y = 270;
        }
        else
        {
            currentRotation.y = 0;
        }
      
        _selectedFace.transform.DOLocalRotate(currentRotation, .2f);

I know I am missing something here but cannot figure out what. Any help is highly appreciated.

EDIT:
Just for clarification, I am wondering why rotating the face on the local Y axis, Unity reports it as rotating on the X axis. Added image to showcase the issue:
Local Rotation With Log

try using Transform.RotateAround(). you can specify which axis to rotate around… specify the world Y axis (the “Normal” vector) for each respective surface.