Fargate [request]: Profiling of Task Launch process

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**Tell us about your request**
Would like to get stats on how much time we are spending during a new task launch on Fargate, for example how much time went into pulling down the image, booting the task, etc.

**Which service(s) is this request for?**
This would be for Fargate

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
We are trying to understand why a particular service and its tasks are taking longer to launch and startup.

**Are you currently working around this issue?**
We filed a support ticket and got information about how much time the task was spending pulling docker image, starting up and other things, that helped us figure out we need to reduce image size, shorten grace period.

**Additional context**
Anything else we should know?

**Attachments**
If you think you might have additional information that you'd like to include via an attachment, please do - we'll take a look. (Remember to remove any personally-identifiable information.)

The issue names no repository files, tests, or entry points; it only requests timing statistics for Fargate task launch stages such as image pulling and task startup. Start by reviewing the request and its support-ticket context, then define the service-level scope and acceptance criteria for exposing those timings.

Written by the indexing model from the issue text.