Using a fully managed database proxy service allows ephemeral compute instances, like AWS Lambda functions, to efficiently manage database connections. This service can absorb the variability in concurrent connections, smoothing out spikes in traffic and preserving backend database stability. It achieves this through connection pooling and multiplexing, which enhances application scalability and resilience without exhausting connections. While other options may improve availability (Multi-AZ) or read performance (Read Replica), they do not offer the specific benefits of a managed proxy service when it comes to connection pooling. Scaling the compute engine vertically would not directly solve the problem of efficiently managing a large number of connections and could lead to resource exhaustion under high traffic conditions.