[EKS/Fargate] [request]: Schedule evenly pod replicas across AZs

**Tell us about your request**
At the time being, we have observed that there is no guarantee that EKS cluster on Fargate schedule pod replicas evenly across multiple Availability Zones.

**Which service(s) is this request for?**
Fargate, EKS

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
We have a fargate profile with 1 namespace and the 2 private subnets. We have a deployment with 2 replicas and we would like that each replica is deployed on a different AZ.
At the time being this behaviour is not guaranteed.

We identified two test cases:
1) Scaling a deployment from 1 replica to 2 replicas: we observed that the 5 times out of 10, the replicas were deployed in the same AZ.

2) Starting from a new deployment configured with 2 replicas: we observed that 3 times out of 10, the replicas were deployed in the same AZ.

**Are you currently working around this issue?**
Currently we are not aware of any workaround.

No repository files, tests, or entry points are identified. Start by reproducing the two described EKS/Fargate scenarios with one namespace, two private subnets, and two replicas, then record AZ placement. Done would mean replicas are reliably scheduled across different Availability Zones rather than co-located.

Written by the indexing model from the issue text.