"The entropy of the probability distribution describing the system" only has meaning if there is an observer to actually hold that probability distribution. Since probability is in the mind, there is no fixed external thing that just "is" the probability distribution of the system.

There are two distinct things; one is "the system" and the other is "the probability distribution over states of the system." If you make an idealization and do math just on "the system" then the distributions in those idealizations are entropy increasing (if you exclude any observer or external stuff to the system). That does not correspond to reality (because the system's not truly closed), but is often a useful approximation for describing "the arrow of time."

If you want to talk about "the probability distribution over states of the system" then you must also be including some observer with a mind of some sort, or else the notion of there being a probability distribution (as opposed to just whatever the deterministic eventuality of whatever does in fact occur) doesn't make semantic sense.

So, to speak about the "probability distribution of the system" there has to be a Maxwell's demon sitting there having that distribution in its mind (e.g. some observer), and whatever entity it is that is dissipating waste heat while doing physical processes to update its beliefs must be increasing entropy.