The project Neon aims to create a new serverless Postgres service with a modern cloud-native architecture. It separates storage and compute to provide an excellent Postgres experience. The team made key decisions such as building their own storage from first principles, separating the WAL and page services, and leveraging cloud object storage for efficient data management. They also designed a system that keeps old page versions efficiently, making PITR operations quick and computationally cheap. This approach allows Neon to provide a robust and cost-efficient platform for running Postgres in the cloud.