What if there was a general mechanism to allow operators to be implemented by user code that does not belong to the class?

If the name [e.g.] __operatorhook_or__ is defined anywhere in a module, within that module all calls to that operator are replaced with a two-step process:

call __operatorhook_or__(dict1, dict2)
if it returns a value, use that value
if it returns NotImplemented use the ordinary operator lookup process, i.e. dict1.__or__ and dict2.__ror___
[if __operatorhook_or__ is not defined, treat the same as if it had returned NotImplemented]

Then a user could simply do:

def __operatorhook_or__(obj1, obj2):
    if isinstance(obj1, dict) and isinstance(obj2, dict):
        return {**obj1, **obj2}
    return NotImplemented

def __operatorhook_ior__(obj1, obj2):
    if isinstance(obj1, dict):
        obj1.update(obj2)
        return obj1
    return NotImplemented