Add API endpoint that lets you see what happened in the backfill

[dstandish]

Body

We can see the backfill entity but it does not show what runs were trigger with it etc.

Committer

• I acknowledge that I am a maintainer/committer of the Apache Airflow project.

[vatsrahul1001]

As discussd with @dstandish this is only good to have. I will look into this later

[shivaam]

Hi @dstandish — I'd like to pick this up.

I started with a prototype in #64089 (adding state counts directly to BackfillResponse), but based on feedback from @uranusjr and thinking through the design, I'm going to take a different approach:

Plan: New GET /backfills/{backfill_id}/dag_runs endpoint

This would return the BackfillDagRun entries with their linked DagRun state, logical_date, and exception_reason (for skipped slots). The UI can then compute progress counts client-side.

Benefits over enriching BackfillResponse:

• Keeps the backfill model stable
• Returns the actual dag run data (not just aggregated counts)
• Enables linking individual dag runs to backfills in the UI
• Supports future CLI airflow backfill status use case

I'll close #64089 and open a new PR with this approach. Let me know if the approach makes sense to you.

[shivaam]

@dstandish published a PR for adding get backfill dag runs api.
#67381