Fargate Task with ECS exec Task Role missing under ECS cluster resource

## Problem

- I have an Amazon ECS Cluster, in which I have deployed an AWS Fargate Task.
- I have associated an IAM Task Role with this Fargate Task that allows [ECS exec](https://aws.amazon.com/about-aws/whats-new/2021/12/aws-toolkit-vs-code-amazon-ecs-exec/) to work (via Systems Manager Agent).
- I can see the ECS Task running in the AWS Management Console.
- I can use the AWS CLI, with Session Manager plugin, to remotely exec a process interactively inside the Fargate Task.
- When I view the ECS Cluster in VSCode, with the AWS Toolkit, I am **unable** to see this Fargate Task. It says "_No Containers Found_"

Screenshot showing missing container in `us-west-2` region:

Screenshot showing successful ECS exec interactive connection to container, via Session Manager:

## Expected behavior

Fargate Tasks should appear under ECS clusters, in the AWS Toolkit.

## System details (run the `AWS: About Toolkit` command)

- OS: MacOS latest
- Visual Studio Code version: 1.87.2
- AWS Toolkit version: 2.17.0

The issue names no files or tests. Start by reproducing the missing Fargate task in the AWS Toolkit's ECS cluster view with the described ECS exec setup, then trace the ECS cluster resource handling. Done means the running Fargate task and its container appear under the cluster.

Written by the indexing model from the issue text.