[I] Add new DAG Run types for: `TriggerDagRunOperator` and `Rest API` [airflow]

[via GitHub]

pedro-cf opened a new issue, #40989:
URL: https://github.com/apache/airflow/issues/40989

   ### Description
   
   Currently DAG Runs triggered via a 
[TriggerDagRunOperator](https://airflow.apache.org/docs/apache-airflow/stable/_api/airflow/operators/trigger_dagrun/index.html#airflow.operators.trigger_dagrun.TriggerDagRunOperator)
 and the [Airflow REST 
API](https://airflow.apache.org/docs/apache-airflow/stable/stable-rest-api-ref.html)
 are categorized with run type "Manual":
   
![image](https://github.com/user-attachments/assets/06290124-98d9-439d-aef2-8e7cffae3431)
   
   Would it be possible to add 2 new types: `TriggerDagRunOperator`  `Rest API` 
?
   
   ### Use case/motivation
   
   Add the ability to distinguish different types of DAG Runs.
   
   ### Related issues
   
   _No response_
   
   ### Are you willing to submit a PR?
   
   - [ ] Yes I am willing to submit a PR!
   
   ### Code of Conduct
   
   - [X] I agree to follow this project's [Code of 
Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)
   


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