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Re:Neon – Serverless Postgres by excuses_ on Saturday May 28, 2022 @02:43AM (#31538134)
Typically it means S3 and alike. Not being bounded by disk size of your server.

Or in their case they might refer to horizontal scalability of their storage layer which is independent from computing.

Re:Neon – Serverless Postgres by nikita on Saturday May 28, 2022 @03:57AM (#31538467)
Yes, you will never run out of storage with Neon. The reason to it that in our tiered storage implementation S3 is the cheapest tier and we will offload data into S3 if it gets too big.