### 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
assert 'test_echo_env_variables' == os.environ['AIRFLOW_CTX_DAG_ID']
        assert 'hive_in_python_op' == os.environ['AIRFLOW_CTX_TASK_ID']
        assert DEFAULT_DATE.isoformat() == os.environ['AIRFLOW_CTX_EXECUTION_DATE']
        assert DagRun.generate_run_id(DagRunType.MANUAL, DEFAULT_DATE) == os.environ['AIRFLOW_CTX_DAG_RUN_ID']
    def test_echo_env_variables(self, dag_maker):
        with dag_maker(
            'test_echo_env_variables',
            start_date=DEFAULT_DATE,
            end_date=DEFAULT_DATE + datetime.timedelta(days=10),
        ):
            op = PythonOperator(task_id='hive_in_python_op', python_callable=self._env_var_check_callback)
        dr = dag_maker.create_dagrun(
            run_type=DagRunType.MANUAL,
            external_trigger=False,
        )
        ti = TI(task=op, run_id=dr.run_id)
        ti.state = State.RUNNING
        session = settings.Session()
        session.merge(ti)
        session.commit()
        ti._run_raw_task()
        ti.refresh_from_db()
        assert ti.state == State.SUCCESS
    @patch.object(Stats, 'incr')
    def test_task_stats(self, stats_mock, create_task_instance):