Just for the record: has anyone already tried an equivalent of the mirror test to current AI models? And if so: results?

Something like: video stream -> AI model -> robot control, place robot in front of mirror, see if AI model 'knows' (plz. define) it's itself that moves robot's arms / head / wheels etc.

The core of consciousness, building in internal model of the external world, is necessary if you want to do any kind of complex interaction with the world. Otherwise you wouldn't have any way to keep track of what's happening (e.g. no object permanence).

All the stuff related to the self is however optional, especially when it comes to AI where the self (bunch of GPUs in a datacenter) doesn't even exist in the problem space the AI is thinking about.

The "stuff related to the self" is consciousness. Your inner life is consciousness. You can easily imagine an "internal model of an external world" without consciousness.