What should a solutions architect do to meet these requirements?

Explanations:

Pointing the client driver at an RDS custom endpoint does not provide the connection pooling capabilities needed to manage unpredictable traffic. Deploying Lambda functions inside a VPC alone does not prevent overloading the database with too many connections.

Pointing the client driver at an RDS proxy endpoint allows for connection pooling and management, which can help in maintaining predictable database performance and reducing the number of direct connections from Lambda functions. Deploying the Lambda functions inside a VPC enables secure access to the RDS instance.

An RDS custom endpoint does not provide the benefits of connection pooling. Deploying Lambda functions outside a VPC will prevent them from securely accessing the private RDS instance, violating security and connectivity requirements.

While an RDS proxy endpoint would help with connection management, deploying the Lambda functions outside a VPC means they cannot access the private RDS instance directly, resulting in connectivity issues.