I didn't read the paper to see what they mean but in my thinking the "cosmological term" in the general action I associated it when it comes to specifically 4D spacetime, can only be understood beyond the "just another parameter" level if we also understand how 4D spacetime emerges, because that is what would somehow factor out that term.
Probably the differences lies in what is meant by emergence. Each time before when I've read Rovelli style papers it was clear that there are different meanings of the concept. I don't believe in any fundamental DOFs. The alterantive concept of emergence is just interacting effective theories, since there is no master theory (since in my view theory attaches to observer machinery), there are no fundamental DOFs. The task thus becomes how to even make something constructure without referring to fundamental DOFs.
The difference for emergence would be in like "emergence FROM something else", or "emergence in terms of just evolution relative to the prior state" where there are no fixed background context at all.
This is even the constructing principle behind the association in my old post. The idea is that the possible future can only be rated in terms of an action measure in terms of a specific reduced time history. This is why P_max < 1, and thus us why the normally unbounded information divergence IS bounded in this case. And this was also the keys that allows the expectation that the term is small, but strictly non-zero as inferred by a finite observer.
So maybe if we focus on the "emergence of spacetime" the cosmo constant problem will be solved automatically, if done the right way. IMO the emergence of spacetime, is an inference, and it's hosted by an observer. Ie. an extension of the essence that Smolin et all mention in the relative locality idea that spacetime is simply a result of an inference from actual data! Now that data needs to be stored and processed by something with finite capacity. This is where alot of things are missing....