Update all images in Cloud Run and all functions in Cloud Functions to send logs to both Cloud Logging and the client's logging service. Ensure that all the ports required to send logs are open in the VPC firewall.

Create a Pub/Sub topic, subscription, and logging sink. Configure the logging sink to send all logs into the topic. Give your client access to the topic to retrieve the logs.

Create a storage bucket and appropriate VPC firewall rules. Update all images in Cloud Run and all functions in Cloud Functions to send logs to a file within the storage bucket.

Create a logs bucket and logging sink. Set the retention on the logs bucket to 365 days. Configure the logging sink to send logs to the bucket. Give your client access to the bucket to retrieve the logs.