How to integrate AWS CloudHSM with a serverless architecture using CloudHSM Client SDK 5?

I’m working on a serverless project and would like to integrate AWS CloudHSM using the AWS CloudHSM Client SDK 5. According to the official documentation, this should be possible, but the page doesn’t include any practical examples or implementation guidance.

Most examples I’ve found involve provisioning an EC2 instance to run the client daemon, which makes sense in a traditional setup. However, it’s unclear how to achieve this in a serverless architecture (e.g., with AWS Lambda or containerized tasks in AWS Fargate). I would prefer a Lambda example, though.

I’m specifically looking to understand:

What are the architectural considerations or limitations when using CloudHSM with serverless compute?

How and where should the CloudHSM client daemon run in a serverless environment?

Is there a supported way to connect from Lambda or Fargate to CloudHSM using the SDK 5?

Any insights, examples, or reference architectures would be helpful.