If you can‘t tell I find issues when terms are taken from psychology and applied to statistics. The terminology should flow in the other direction, from statistics and into psychology.
So my background is that I have done both undergraduate in both psychology and in statistics (though I dropped out of statistics after 2 years) and this is the first time I hear about artificial cognition, so I don‘t think this term is popular, and a short internet search seems to confirm that suspicion.
Out of context I would guess artificial cognition would mean something similar to cognition as artificial neural networks do to neural networks, that is, these are models that simulate the mechanisms of human cognition and recreate some stimulus → response loop. However my internet search revealed (thankfully) that this is not how researches are using this (IMO misguided) term.
https://psycnet.apa.org/record/2020-84784-001
https://arxiv.org/abs/1706.08606
What the researchers mean by the term (at least the ones I found in my short internet search) is not actual machine cognition, nor claims that machines have cognition, but rather an approach of research which takes experimental designs from cognitive psychology and applies them to learning models.