got it - on ECS hybrid you could set up a datadog sidecar that does this:
https://docs.datadoghq.com/integrations/ecs_fargate/?tab=webui
But we don't offer sidecar-level customization on serverless. We do expose the raw compute logs for each op over our API, but getting that to be streaming would be tricky. I'll check with the team to see if we have any other options here.