In #43015, a new Task Execution API-server was added. This can be run with the Core Airflow APIs and can also be run separately.
To run all apis
airflow api-server
# Alternate
airflow api-server --apps all
# Alternate
airflow api-server--apps core,execution
E.g to only run Task execution API
airflow api-server --apps execution
The doc should contain details of our recommendation.