### Apache Airflow version

2.2.3rc1 (release candidate)

### What happened

I ran a DAG that does nothing explicitly with context, so I'm surprised to see deprecation warnings about context being used (trimmed to cut down on noise):

```
baseoperator.py:1107 DeprecationWarning: Accessing 'execution_date' from the template is deprecated and will be removed in a future version. Please use 'data_interval_start' or 'logical_date' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'next_ds' from the template is deprecated and will be removed in a future version. Please use '{{ data_interval_end | ds }}' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'next_ds_nodash' from the template is deprecated and will be removed in a future version. Please use '{{ data_interval_end | ds_nodash }}' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'next_execution_date' from the template is deprecated and will be removed in a future version. Please use 'data_interval_end' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'prev_ds' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'prev_ds_nodash' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'prev_execution_date' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'prev_execution_date_success' from the template is deprecated and will be removed in a future version. Please use 'prev_data_interval_start_success' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'tomorrow_ds' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'tomorrow_ds_nodash' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'yesterday_ds' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'yesterday_ds_nodash' from the template is deprecated and will be removed in a future version.
```

### What you expected to happen

I'd only expect to see deprecation warnings about things my DAG is actually interacting with.

### How to reproduce

Run this DAG:

```python
from datetime import datetime

from airflow import DAG
from airflow.operators.bash import BashOperator

with DAG(
    dag_id="no-context", schedule_interval=None, start_date=datetime(2021, 12, 10)
) as dag:
    BashOperator(task_id="sleep", bash_command="echo 'Hello!'")
```

Note: I also tried a TaskFlow DAG and that wasn't impacted.

### Operating System

MacOS 11.6

### Versions of Apache Airflow Providers

_No response_

### Deployment

Virtualenv installation

### Deployment details

_No response_

### Anything else

This was introduced in #19886 (cc @uranusjr).

### Are you willing to submit PR?

- [ ] 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)

tests/models/test_taskinstance.py
with dag_maker(dag_id='test_not_requeue_non_requeueable_task_instance'):
            task = BaseSensorOperator(
                task_id='test_not_requeue_non_requeueable_task_instance_op',
                pool='test_pool',
            )
        ti = dag_maker.create_dagrun(execution_date=timezone.utcnow()).task_instances[0]
        ti.task = task
        ti.state = State.QUEUED
        with create_session() as session:
            session.add(ti)
            session.commit()
        all_deps = RUNNING_DEPS | task.deps
        all_non_requeueable_deps = all_deps - REQUEUEABLE_DEPS
        patch_dict = {}
        for dep in all_non_requeueable_deps:
            class_name = dep.__class__.__name__
            dep_patch = patch(f'{dep.__module__}.{class_name}.{dep._get_dep_statuses.__name__}')
            method_patch = dep_patch.start()
            method_patch.return_value = iter([TIDepStatus('mock_' + class_name, True, 'mock')])
            patch_dict[class_name] = (dep_patch, method_patch)
        for class_name, (dep_patch, method_patch) in patch_dict.items():
            method_patch.return_value = iter([TIDepStatus('mock_' + class_name, False, 'mock')])
            ti.run()
            assert ti.state == State.QUEUED
            dep_patch.return_value = TIDepStatus('mock_' + class_name, True, 'mock')
        for (dep_patch, method_patch) in patch_dict.values():
            dep_patch.stop()
    def test_mark_non_runnable_task_as_success(self, create_task_instance):