Run DB check only for core components in prod entrypoint

[shaealh]

Closes #60271

Restrict entrypoint DB check to scheduler, dag-processor, triggerer, and api-server. Skip DB check for worker/task/interactive commands to avoid direct metadata DB dependency in worker pods.

[potiuk]

Very nice ! Thank you :)

[potiuk]

Let's see if CI agrees :D

[potiuk]

Somethig wrong - likely the check is somewhat wrong - the logs of failing tests can be downloaded as artifacts @shaealh

[potiuk]

@shaealh This PR has been converted to draft because it does not yet meet our Pull Request quality criteria.

Issues found:

• ❌ Kubernetes tests: Failing: Kubernetes tests / K8S System:KubernetesExecutor-3.10-v1.30.13-true, Kubernetes tests / K8S System:KubernetesExecutor-3.10-v1.30.13-false, Kubernetes tests / K8S System:CeleryExecutor-3.10-v1.30.13-true, Kubernetes tests / K8S System:CeleryExecutor-3.10-v1.30.13-false, Kubernetes tests / K8S System:LocalExecutor-3.10-v1.30.13-true (+1 more). See the K8s testing documentation. See Kubernetes tests docs.

Note: Your branch is 6 commits behind main. Some check failures may be caused by changes in the base branch rather than by your PR. Please rebase your branch and push again to get up-to-date CI results.

What to do next:

• The comment informs you what you need to do.
• Fix each issue, then mark the PR as "Ready for review" in the GitHub UI - but only after making sure that all the issues are fixed.
• Maintainers will then proceed with a normal review.

Converting a PR to draft is not a rejection — it is an invitation to bring the PR up to the project's standards so that maintainer review time is spent productively. If you have questions, feel free to ask on the Airflow Slack.

[shaealh]

Thank you @potiuk, fixed the issue and marked the PR as "Ready for review"

[shaealh]

Cannot merge, need reviewer to confirm and merge