Well here's the thing: The onus on you is to produce a "physical theory" that describes some subset of the computations of a 4D CA and which can explain (or posit or hypothesize if you will) properties of observers (in that kind of world), and properties of the space that they observe, which would be self-consistent and descriptive of "interesting, constrained, lifelike behaviour and interaction with environment and sentient representation of environment aspects" etc.
I'm not sure I really understand what you're asking for here. I'm applying the very same concepts of "lifelike" and "sentient" that I apply to configurations of matter here in our own universe. These concepts certainly have to do with the things you mention - perception of surrounding environment, information processing, the building of internal representations, action within the environment, etc. All of these concepts are essentially computational, and are highly general. They should be applicable to substructures in any computation-universal system.
If you're asking how we would be able to recognize SASs (or even just lifelike substructures) in a 4D cellular automata, there's clearly no simple answer to that question. We can imagine running a giant computer implementation of a 4D world, with lots of software tools at our disposal. Obviously, we could examine the state of any bit in the lattice, and we could also build higher-level pattern-matching tools that would help us to recognize higher-level structures (like gliders, and perhaps larger molecule-like structures). To recognize lifelike substructures in the lattice, we would bring everything we know about computation, self-replication, information processing, etc., to bear on the subject. We already have some conception of what a self-replicating structure in Conway's Life universe would look like. I don't see any reason why we couldn't recognize such things if they arose naturally in some 4D CA that we were studying.
I have no doubt that the problem would be difficult. I am also fully aware that we have no precise "definition" which infallibly distinguishes all "living" sub-structures from "non-living" ones. This is true for any universe, including our own. We know that elephants are intelligent, but do we really have a clear picture of what kind of sentience they possess? The science-fiction author Stanislaw Lem suggests that alien intelligences in our own universe might be as big as galaxies, and might look to us simply like clouds of cosmic dust.
My guess is that that physical theory (and that subset of computations or computed states) would end up being proven to
be essentially equivalent to the physical theory of OUR universe.
We may be starting a game of what Dennett calls "burden tennis", but it seems to me that the burden is entirely upon you to support such an extraordinary claim. Are you suggesting that, for any CA we discover that contains SASs, if we analyze how those SASs gain information about their environment and how they affect it, if we analyze how their environment must seem *to them*, we will find that it looks essentially like our own quantum-physical, relativistic universe? I find that highly implausible, to put it mildly.
Maybe you're simply arguing that our definitions of "life" and "sentience" are so tied to our particular physics that we simply wouldn't find SASs when we explore CA worlds. (Or, we'd only find them in those CA that manage to behave very much like our own universe, with QM and GR and all the rest.) Again, I find that highly implausible. I think our standard (fuzzy) conceptions of life and sentience are substantially more "substrate neutral" than that.
You can't just say "there could be life and sentience in this (arbitrarily weird) set of constraints" and then not bother to
define what you mean by life and sentience. They aren't self-explanatory concepts. Our definitions of them only apply
within universes that behave at least roughly as ours does.
As I've said, my definitions of life and sentience are essentially computational, and they're the same ones I apply to groups of molecules in our own local universe. I think these definitions are applicable within any universes that are computation-universal.
Of course, it should be obvious that my position rests on underlying positions about the possibility of computational models of life, consciousness, etc. If you don't believe, for instance, that hard-AI is possible, even in principle, then obviously you won't accept my conclusions, at least when it comes to intelligent SASs. But in that case, we're really talking past each other, and we need to back up - way up. (And frankly, I'm not interested in backing up that far.)