Make available user who triggered the DAG manually in dag_run.conf

### Description

Hello everyone
It should be possible to read out the user name that started a DAG manually.
This user name is required to enter it in the ModifiedBy field during a database update and to display it in the log file for auditing purposes.
If a DAG is started automatically by the scheduler, this field should contain “scheduler”.
Many thanks

### Use case/motivation

The user name is needed for audit purposes.
e.g. triggered_by = context['dag_run'].conf.get('triggered_by', 'unknown')

### 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)

Start by tracing how dag_run.conf and context['dag_run'] are populated for manually triggered and scheduler-created DAG runs. Define coverage for both trigger paths, then verify that the resulting user value is available for audit logging and database updates, with scheduler-triggered runs using the requested fallback.

Written by the indexing model from the issue text.