Certainly there's no fundamental physical law which talks about part-whole relations. "Spatial part" is a higher-order concept. But it's still an utterly basic one. If I say "the proton is part of that nucleus", that's a physically meaningful statement.

We might have avoided this digression if, instead of part-whole relations, I'd mentioned something like "spatial and temporal adjacency" as an example of the "modes of combination" of fundamental entities which exist in physical ontology. If you take the basic physical reality to be "something at a point in space-time" (where something might be a particle or a bit of field), and then say, how do I conceptually build up bigger, more complicated things? - you do that by putting other somethings at the space-time points "next door" - locations adjacent in space, or upstream/downstream in time.

There are other perspectives on how to make complexity out of simplicity in physics. A more physical perspective would look at interaction, and separate objects becoming dynamically bound in some way. This is the basis of Mario Bunge's philosophy of systems (Bunge was a physicist before he became a philosopher); it's causal interaction which binds subsystems into systems.

So, trying to sum up, we can say that the modes of combination of basic entities in physics have a non-causal aspect - connectedness, being next to each other, in space and time - and a causal aspect - interaction, the state of one affecting the state of another. And these aspects are even related, in that spatiotemporal proximity is required for causal interaction to occur.

Finally, returning to your question - how do I expect physical ontology to change - part of the answer is that I expect the elementary non-causal bindings between things to include options besides spatial adjacency. Spatial proximity builds up spatial geometry and spatially extended objects. I think there will be ontological complexes where the relational glue is something other than space, that conscious states are an instance of this, and that such complexes show up in our present physics in the form of entanglement. Going back to the language of monads - spatial relations are inter-monadic, but intra-monadic relations will be something else.

In physics, if A is part of B, it means it's a spatial part. I think the "parts" of a conscious experience are part of it in some other way. I say this very metaphorically, and only metaphorically, but it's more like the way that polyhedra have faces. The components of a conscious experience, I would think, don't even occur independently of conscious experiences.

There's a whole sub-branch of ontology concerning part-whole relations, called mereology. It potentially encompasses not only spatial parts, but also subsets, "logical parts", "metaphysical parts" (e.g. the property is part of the thing with the property), the "organic wholes" of various holisms, and so on. Of course, this is philosophy, so you have people with sparse ontologies, who think most of this is not really real, and then you have the people who are realists about various abstract or exotic relations.

I think I've invented a name for my own ontological position, by the way - reverse monism. I'll have to explain what that means somewhere...