The major part of what Neon does is remove the file system abstraction that is between that Storage and Compute, so that we can better utilize the available resources because we can better select what information is or isn't being lost.
A good example of what removing the file system abstraction enables for us is effectively free PITR, (lagging) replicas, and data branching. This is because PostgreSQL's file-system-based storage engine expects to be the only one working on the data directory, which means that any FS attached to a replica cannot be shared. If you remove that file-system based storage engine and plug in a different storage engine, those expectations are removed too, and after some effort integrating into the smgr-APIs, we're now able to provide a storage layer that only needs to contain one copy of the data for N physical replicas, instead of N copies.