### 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
TaskInstance as TI,
    TaskReschedule,
    Variable,
    XCom,
)
from airflow.models.taskinstance import load_error_file, set_error_file
from airflow.operators.bash import BashOperator
from airflow.operators.dummy import DummyOperator
from airflow.operators.python import PythonOperator
from airflow.sensors.base import BaseSensorOperator
from airflow.sensors.python import PythonSensor
from airflow.serialization.serialized_objects import SerializedBaseOperator
from airflow.stats import Stats
from airflow.ti_deps.dependencies_deps import REQUEUEABLE_DEPS, RUNNING_DEPS
from airflow.ti_deps.dependencies_states import RUNNABLE_STATES
from airflow.ti_deps.deps.base_ti_dep import TIDepStatus
from airflow.ti_deps.deps.trigger_rule_dep import TriggerRuleDep
from airflow.utils import timezone
from airflow.utils.db import merge_conn
from airflow.utils.session import create_session, provide_session
from airflow.utils.state import State, TaskInstanceState
from airflow.utils.types import DagRunType
from airflow.version import version
from tests.models import DEFAULT_DATE, TEST_DAGS_FOLDER
from tests.test_utils import db
from tests.test_utils.asserts import assert_queries_count
from tests.test_utils.config import conf_vars
from tests.test_utils.db import clear_db_connections, clear_db_runs
@pytest.fixture
def test_pool():