aws ssm start-session fails with TargetNotConnected on ECS on Fargate

I have ECS running with Fargate launchtype: the containers are running successfully, however to troubleshoot/debug an issue I tried the
AWS ECS Exec, however while trying with the https://github.com/aws-containers/amazon-ecs-exec-checker all checks are passed, it only shows in red
```
Managed Agent Status
----------
1. STOPPED (Reason: null) for "containernameredacted" - LastStartedAt: null
```
Since there are many reports of ECS Exec not working & based on this comment https://github.com/aws/amazon-ssm-agent/issues/361#issuecomment-1007335151 I tried using the

aws ssm start-session --target ecs:.... but it throws TargetNotConnected error,
```

aws ssm start-session --target ecs:clusternameredacted_e7e36d0d4e744104bd4d225c44daddfe_e7e36d0d4e744104bd4d225c44daddfe-3839356491

An error occurred (TargetNotConnected) when calling the StartSession operation: ecs:clusternameredacted_e7e36d0d4e744104bd4d225c44daddfe_e7e36d0d4e744104bd4d225c44daddfe-3839356491 is not connected
```
so my questions is

- is it not possible to connect to containers running on ECS with fargate launchtype
- Is any config missing for the aws ssm start-session for ECS Fargate?
If somebody has already faced this targetnotconnected for ssm start-session please do guide on the solution?

Start by reproducing the reported `aws ssm start-session --target ecs:...` command and reviewing the ECS Exec Checker output, especially the STOPPED managed agent status. Determine from the agent and ECS integration entry points whether Fargate targets are expected to support this session path and identify the configuration or documentation needed to explain the TargetNotConnected result.

Written by the indexing model from the issue text.