Filter stale Dag tags from public API (#66827)

[deepujain]

Title: Filter stale Dag tags from public API (#66827)

Summary

The public Dag tags endpoint returned tag names directly from dag_tag, so tags attached only to stale Dags could remain visible in the UI filter after the Dag file was removed. This filters tags through non-stale DagModel rows while preserving tags that are still attached to active Dags.

Changes

• airflow-core/src/airflow/api_fastapi/core_api/routes/public/dag_tags.py -- join DagTag through DagModel and exclude stale Dag rows before grouping tag names.
• airflow-core/tests/unit/api_fastapi/core_api/routes/public/test_dag_tags.py -- add a stale-only tag case while keeping a shared active/stale tag to prove active tags are not dropped.

Screenshot

Test plan

• ruff format --check airflow-core/src/airflow/api_fastapi/core_api/routes/public/dag_tags.py airflow-core/tests/unit/api_fastapi/core_api/routes/public/test_dag_tags.py
• ruff check airflow-core/src/airflow/api_fastapi/core_api/routes/public/dag_tags.py airflow-core/tests/unit/api_fastapi/core_api/routes/public/test_dag_tags.py
• AIRFLOW_HOME=/private/tmp/airflow-test-66827 uvx --from uv==0.11.21 uv run --project airflow-core pytest airflow-core/tests/unit/api_fastapi/core_api/routes/public/test_dag_tags.py::TestDagTags::test_get_dag_tags -xvs --with-db-init
• CI passes

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

• Yes (OpenAI Codex)

Generated-by: OpenAI Codex following the guidelines

Fixes #66827

[shahar1]

@deepujain please note that you (or your operator) should include AI attribution in the PR as we state in the AI guidelines.
This PR, as well as others, are blocked from being merged until this is corrected.
Please be warned that creating additional PRs except for the 10 you've already created (listed below) without addressing the above might cause in a permanent block from Apache organization on GitHub.

List of PRs:

• #69161
• #69159
• #69158
• #69157
• #69156
• #69154
• #69153
• #69152
• #69151
• #25461

AI attribution addressed

[pierrejeambrun]

LGTM, working as expected, tested locally.

Just one suggestion, good to merge after that.

[deepujain]

Removed airflow-core/newsfragments/69156.bugfix.rst as requested. This follow-up is deletion-only, and git diff --check is clean.

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Drafted-by: OpenAI Codex (no human review before posting)