### Description

Introducing a startupProbe onto the airflow services would be useful for slow starting container and most of all it doesn't have side effects.

### Use case/motivation

We have an internal feature where we perform a copy of venv from airflow services to cloud storages which can sometimes take a few minutes. Copying of a venv is a metadata heavy load: https://learn.microsoft.com/en-us/troubleshoot/azure/azure-storage/files-troubleshoot-performance?tabs=linux#cause-2-metadata-or-namespace-heavy-workload.

Introducing a startupProbe onto the airflow services would be useful for slow starting container and most of all it doesn't have side effects.

### Related issues

_No response_

### Are you willing to submit a PR?

- [X] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

docs = render_chart(
            values={"dags": dags_values},
            show_only=["templates/scheduler/scheduler-deployment.yaml"],
        )
        assert "git-sync" in [c["name"] for c in jmespath.search("spec.template.spec.containers", docs[0])]
        assert "git-sync-init" in [
            c["name"] for c in jmespath.search("spec.template.spec.initContainers", docs[0])
        ]
    @pytest.mark.parametrize(
        "dag_processor, executor, skip_dags_mount",
        [
            (True, "LocalExecutor", False),
            (True, "CeleryExecutor", True),
            (True, "KubernetesExecutor", True),
            (True, "LocalKubernetesExecutor", False),
            (False, "LocalExecutor", False),
            (False, "CeleryExecutor", False),
            (False, "KubernetesExecutor", False),
            (False, "LocalKubernetesExecutor", False),
        ],
    )
    def test_dags_mount_and_gitsync_expected_with_dag_processor(