I will explain what Nile tries to do. Happy to follow up.
The most foundational element in SaaS is a tenant. It makes a lot of sense to build this core concept into the database. Imagine having a lot of virtual tenant databases that can be co-located on one physical Postgres (multi-tenant) for better cost, and some of them can be placed on a dedicated database for better isolation. The virtual tenant DBs can be located anywhere on the planet for low latency or compliance. The client can route to the right tenant seamlessly without routing logic in the application.
Isolating tenants into their own virtual DBs is great, but you will also want to be able to share data across tenants where it makes sense. Backups should be available for each tenant, and it should be possible to restore them instantaneously. Schema changes should be applied seamlessly across all the tenant DBs, and it should also be possible to do staged rollouts for different tenant tiers. While supporting all this, all the standard SQL capabilities should work across the tenants for admin operations. All the standard Postgres tooling should work. You want the experience of a single Postgres.
This is what Nile tries to achieve. A model that gives you fine-grained control over your tenants. You create, scale, locate, pay all by tenants.