Aurora Postgres does still have VACUUM, which seems to work in the same way -- which is the same in Neon. AWS have in the past promoted Aurora as having significantly better performance characteristics when VACUUM is run. That may well be true, but the benefits seem to come from not having to generate full page writes in WAL, which are a way of preventing a low-level problem called torn pages. Theoretically you could just turn off full-page writes in standard Postgres if you had hardware that offered atomic page writes, though I don't think that it's a widespread practice.
I spend most of my time working on problems with VACUUM in Postgres itself (I'm one of the committers). An approach to organizing storage within transactional constraints seems necessary to push vacuuming down to storage, and that would more than likely need plenty of work in Postgres itself to be practical -- since it would cross a few layers of abstraction. Currently heapam doesn't specifically try to keep tuples inserted around the same time together, so it's hard to make anything that VACUUM does work implicitly or logically.
Disclaimer: I work for Neon
In Postgres, the on-disk representation is virtually the same thing as the in-memory representation used by pages stored in the buffer cache. In a system like Aurora or Neon, the representation of pages in the buffer cache is identical to that of Postgres (or has very minimal divergence to deal with one or two isolated problems). That part doesn't really change, which makes it possible to have a very deep level of compatibility without much effort. So it's radically different in one narrow, scoped way, but otherwise very similar.
While the storage knows how to materialize pages on demand, these are not transactionally consistent pages -- they often need to be interpreted by using metadata about transaction commit status, just like in Postgres.
It would be cool to push down at least parts of the VACUUM down to the storage layer, but it would require more invasive changes Postgres code, which we try to avoid. Maybe in the future. Ideally though, I'd like to improve PostgreSQL itself, to reduce the need for VACUUM in the first place.
Disclaimer: Neon co-founder
Would you ever consider supporting the orioleDB extension in the future?