Fix dag.test() callbacks missing context["exception"]

[Vamsi-klu]

task_runner.main() (the subprocess path) sets context["exception"] = error immediately after run() and before finalize() so failure/retry callbacks can read the raised exception from context. The in-process supervisor used by dag.test() did not mirror that contract, so on_failure_callback and on_retry_callback saw context["exception"] as missing/None when invoked via dag.test(). This patches InProcessTestSupervisor.start() to mirror the subprocess path.

Tests

• Unit regression in test_supervisor.py::TestInProcessTestSupervisor::test_start_sets_exception_in_context_before_finalize (parametrized over FAILED and UP_FOR_RETRY) — verified to fail without the fix and pass with it.
• End-to-end dag.test() regression in test_dag.py::TestDag::test_dag_test_failure_callback_receives_exception_in_context.

closes: #64568

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Was generative AI tooling used to co-author this PR?

• Yes — Claude Code (Opus 4.7)

Generated-by: Claude Code (Opus 4.7) following the guidelines

[ASk1]

@Vamsi-klu can you close your PR, I have made the fix and waiting for the PR #64568 approval for merge and close this issue.

[potiuk]

@Vamsi-klu A few things need addressing before review — see our Pull Request quality criteria.

• ❌ Pre-commit / static checks — Failing: CI image checks / Static checks. See docs.

No rush.

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Note: This comment was drafted by an AI-assisted triage tool and may contain mistakes. Once you have addressed the points above, an Apache Airflow maintainer — a real person — will take the next look at your PR. We use this two-stage triage process so that our maintainers' limited time is spent where it matters most: the conversation with you.

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Drafted-by: Claude Code (Opus 4.7); reviewed by @potiuk before posting

[Vamsi-klu]

@potiuk I apologize for making it ready for review without checking the status of test runs. Will raise a revision in couple of days max. Thanks!

@Vamsi-klu A few things need addressing before review — see our Pull Request quality criteria.

• ❌ Pre-commit / static checks — Failing: CI image checks / Static checks. See docs.

No rush.

---

Note: This comment was drafted by an AI-assisted triage tool and may contain mistakes. Once you have addressed the points above, an Apache Airflow maintainer — a real person — will take the next look at your PR. We use this two-stage triage process so that our maintainers' limited time is spent where it matters most: the conversation with you.

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Drafted-by: Claude Code (Opus 4.7); reviewed by @potiuk before posting