StarshipDagHistoryMigrationOperator does not migrate Run Configs to the target DAG runs

[hkc-8010]

Bug details:
It appears that StarshipDagHistoryMigrationOperator may have a limitation where it does not migrate DAG run run_config fields. The source (AWS MWAA) DAG runs have non-null run_config values, but after the migration to the target environment (Astro), the DAG runs have a run_config value of None.

Source: MWAA, local instance using Astro CLI or any Airflow instance

Destination: Astro

Airflow Version: Replicated the issue on 2.9.2 but applicable for all the Airflow versions.

Starship Version: Latest version 2.1.0

Desktop (please complete the following information):

• OS: iOS
• Browser: ARC
• • Version 1.70.0 (56062)
• • Chromium Engine Version 131.0.6778.86

Screenshots:

• Source dag_run run config:

• Target dag_run run config:

Logs:
No errors in the logs

Additional context

• Expected behavior:
  Given a source DAG run with a non-null run_config, after running the migration operator logic, the target DAG run should include the same run_config.

• Observed behavior:
  Given a source DAG run with a non-null run_config, after the migration operator logic, the target DAG run’s run_config is None.

The migration logic appears to omit run_config during the creation of new DAG runs. Please advise if run_config fields are expected to be migrated or if there's an additional configuration required.