ecs: Bottlerocket support for AsgCapacityProvider

### Describe the bug

I have this C# code that is defining Auto-Scaling group for ECS cluster with Amazon Image:

```C#
_cluster.AddAsgCapacityProvider(new AsgCapacityProvider(this, "asg-provider", new AsgCapacityProviderProps
{
AutoScalingGroup = new AutoScalingGroup(this, "auto-scaling", new AutoScalingGroupProps
{
AutoScalingGroupName = _clusterName,
Vpc = _vpc,
InstanceType = InstanceType.Of(InstanceClass.T3, InstanceSize.NANO),
MinCapacity = 0,
MaxCapacity = 5,
MachineImage = EcsOptimizedImage.AmazonLinux2023(),
InstanceMonitoring = Monitoring.DETAILED,
SecurityGroup = ConstructSecurityGroup(),
Role = CreateInstanceRole()
}),
CapacityProviderName = _clusterName,
EnableManagedTerminationProtection = false,
EnableManagedDraining = false,
EnableManagedScaling = false
}), new AddAutoScalingGroupCapacityOptions());
```

Security Group defines all requested connections. Role is defining everything that the ECS instance needs to work. Once the instance is created by ASG, is automtically registered with the ECS cluster and it's working. It is there, task is deployed, I can connect to the instance.

However if I change the `MachineImage` to `new BottleRocketImage()` as [described in cdk docs](https://docs.aws.amazon.com/cdk/api/v2/docs/aws-cdk-lib.aws_ecs-readme.html#bottlerocket), the registration of new EC2 instace stops working.

### Expected Behavior

Bottlerocket instances should automatically register to the ECS cluster.

### Current Behavior

Bottlerocket instance is created by ASG, but is not registered with the ECS cluster.

### Reproduction Steps

Create a new ECS cluster with ASG as described above and select Bottlerocket as Machine Image.

### Possible Solution

_No response_

### Additional Information/Context

_No response_

### CDK CLI Version

2.131.0

### Framework Version

_No response_

### Node.js Version

20.10.0

### OS

Fedora 39

### Language

.NET

### Language Version

.NET 8

### Other information

_No response_

Start at the AsgCapacityProvider and BottleRocketImage entry points referenced in the issue, then trace how the Bottlerocket machine image is configured for ECS registration. Reproduce the ASG setup with BottleRocketImage and compare it with AmazonLinux2023; done means a Bottlerocket instance created by the capacity provider automatically registers with the ECS cluster.

Written by the indexing model from the issue text.