Is Capacity Provider attached to `cluster` not `service` or `taskdefinition`?

I am using ECS on EC2

What I want to do is like this below.

• task1 (admin task - light)

  • nginx container
  • django python framework container

• task2 (AI task - heavy)

  • api container (access from django container in task1 only)
  • AI model container

So my idea is

cluster - service1 - taskdefinition1 - task1  (use small instance) 
        - service2 - taskdefinition2 - task2  (use big instance)

then At first, I made one capacity provider for admin task

const adminAutoScalingGroup = new autoscaling.AutoScalingGroup(this, 'ASG', {
  vpc,
  instanceType: new ec2.InstanceType('t2.small'),
  machineImage: ecs.EcsOptimizedImage.amazonLinux(),  
  autoScalingGroupName:`ol-${targetEnv}-asg`,
  minCapacity:1,
  maxCapacity:3,
  vpcSubnets: {subnetType: ec2.SubnetType.PUBLIC }
});
const adminCapacityProvider = new ecs.AsgCapacityProvider(this, 'AsgCapacityProvider', {
  autoScalingGroup:adminAutoScalingGroup,
  capacityProviderName: `admin-${targetEnv}-cp`
});

cluster.addAsgCapacityProvider(adminCapacityProvider);// it is attached to cluster?????

I am confused.

capacityprovider should be attached to cluster not service or taskdefinition?

If so, is my idea (make two capacity providers and attach each to each task or service) wrong?.

Is there any best practice for this case?(including fargate)

capacityprovider are defined for clusters. But a cluster can have multiple capacity providers. Thus in your service you can define capacityProviderStrategy which can choose between different providers in the cluster.