Tasks within task groups are not scheduled independently

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I have a DAG that's defined similar to the following

from airflow.models.dag import DAG
from airflow.utils.task_group import TaskGroup
from airflow.operators.python import PythonOperator
from airflow.operators.bash import BashOperator
from tasks import do_s1, do_s2, do_s3


with DAG(dag_id='MyDAG') as dag:
    start = BashOperator(task_id="start", bash_command="echo start")
    end = BashOperator(task_id='end', bash_command="echo end")
    for i in range(5):
        human = i + 1
        with TaskGroup(f'TG{human}') as process_data:
            s1 = PythonOperator(task_id=f'TG{human}_S1', python_callable=do_s1)
            s2 = PythonOperator(task_id=f'TG{human}_S2', python_callable=do_s2, do_xcom_push=False)
            s3 = PythonOperator(task_id=f'TG{human}_S3', python_callable=do_s3, do_xcom_push=False)
            s1 >> s2 >> s3
        start >> process_data >> end

The overall Airflow parallelism is set to 3 and the DAG concurrency is set to 3.
When this runs, the execution sequence is:
TG1_S1
TG2_S1
TG3_S1
TG4_S1
TG5_S1
TG1_S2
TG2_S2
TG3_S2
TG4_S2
TG5_S2
TG1_S3
TG2_S3
TG3_S3
TG4_S3
TG5_S3

After Airflow has started executing the DAG and filled the parallel slots at the beginning, I want it to prioritize finishing a task group before starting another one. So something like this:

TG1_S1
TG2_S1
TG3_S1
TG1_S2
TG2_S2
TG1_S3
TG3_S2
TG2_S3
TG3_S3
TG4_S1
TG5_S1
TG4_S2
TG4_S3
TG5_S2
TG5_S3

So the logic for scheduling the next task should be:
If there is a task group in progress with no running tasks then schedule the next task in that task group
else start executing the tasks in a new task group

What can I do to configure my DAG to run this way?