Public SSM parameter and CloudFormation

Yes, your stack won't be automatically updated when the parameter value changes (which is desired behavior I think).

From https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/dynamic-references.html

CloudFormation doesn't currently support drift detection on dynamic references. For ssm dynamic references where you haven't specified the parameter version, we recommend that, if you update the parameter version in SSM, you also perform a stack update operation on any stacks that include the ssm dynamic reference, in order to fetch the latest parameter version.

One way to trigger the update, could be listing the version of parameter you want to use and then update when you are ready for an update. You can find the latest available version in parameter details.

$ aws ssm get-parameters --names /aws/service/ecs/optimized-ami/amazon-linux-2/recommended/image_id --region us-east-1
{
    "Parameters": [
        {
            "Name": "/aws/service/ecs/optimized-ami/amazon-linux-2/recommended/image_id",
            "Type": "String",
            "Value": "ami-04215982dedb895b4",
            "Version": 123,
            "LastModifiedDate": "2023-10-26T21:03:08.758000+03:00",
            "ARN": "arn:aws:ssm:us-east-1::parameter/aws/service/ecs/optimized-ami/amazon-linux-2/recommended/image_id",
            "DataType": "text"
        }
    ],
    "InvalidParameters": []
}