No Idea, how to access the class, but if the operator is written in Python, you can find its code. There is a bunch of operators in Blender's installation folder(on Windows they are at C:\Program Files\Blender Foundation\Blender 4.0\4.0\scripts\startup\bl_operators) So you can just copy the code defining the operator, change it and register it again. This works as we see from the tooltip that I changed for Select Camera operator:

If the operator is not written in Python, it seems it's no longer possible to override it this way in recent versions:

That's what happens if I try to register an operator with mesh.primitive_cube_add bl_idname.
It used to be possible in previous versions and was useful in some cases. You can still write a new operator entirely and change the UI and keymap to replace some operator, but that's a lot of work.