The correct service for the described scenario is Amazon RDS Proxy. It allows legacy applications to pool and share database connections, reducing the stress on the database's compute and memory resources when handling many simultaneous connections, which is particularly beneficial during traffic surges. Amazon RDS Proxy functions as a proxy layer between the application and the database layer, enhancing scalability and resilience. The other listed services do not offer proxy capabilities for relational databases, nor are they designed to handle database connections and related scalability in this context.