### 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/conftest.py
"""
    Use freezegun to "stub" sleep, so that it takes no time, but that
    ``datetime.now()`` appears to move forwards
    If your module under test does ``import time`` and then ``time.sleep``::
        def test_something(frozen_sleep):
            my_mod.fn_under_test()
    If your module under test does ``from time import sleep`` then you will
    have to mock that sleep function directly::
        def test_something(frozen_sleep, monkeypatch):
            monkeypatch.setattr('my_mod.sleep', frozen_sleep)
            my_mod.fn_under_test()
    """
    freezegun_control = None
    def fake_sleep(seconds):
        nonlocal freezegun_control
        utcnow = datetime.utcnow()
        if freezegun_control is not None:
            freezegun_control.stop()
        freezegun_control = freezegun.freeze_time(utcnow + timedelta(seconds=seconds))
        freezegun_control.start()
    monkeypatch.setattr("time.sleep", fake_sleep)
    yield fake_sleep
    if freezegun_control is not None:
        freezegun_control.stop()
@pytest.fixture(scope="session")
def app():