How would this product compare to a PostgREST based approach (this is the cool tech behind the original supabase) with load balancing at the HTTP level?
Their load balancer is still at the Postgres layer though. You can think of it as just an application that happens to speak a specific API. Load balancing applications is a solved problem.
PostgREST doesn't provide a replacement, rather a subset of the SQL language meant to be safe to expose to untrusted (frontend) clients.
Load balancing is not built-in currently, but it can be done at the proxy layer, taking the advantage that GET/HEAD requests are always executed on read only transactions, so they can be routed to read replicas. This is what Supabase does [1] for example.
[1]: https://supabase.com/docs/guides/platform/read-replicas#api-...