You can pass {job_id}} and {{run_id}} in Job arguments and print that information and save into wherever its needed
please find below the documentation for the same
https://docs.databricks.com/data-engineering/jobs/jobs.html#task-parameter-variables
{{job_id}}
The unique identifier assigned to a job
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{{run_id}}
The unique identifier assigned to a job run
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{{parent_run_id}}
The unique identifier assigned to the run of a job with multiple tasks.
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{{task_key}}
The unique name assigned to a task thatโs part of a job with multiple tasks.