### 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)

airflow/models/baseoperator.py
from airflow.models.base import Operator
from airflow.models.param import ParamsDict
from airflow.models.pool import Pool
from airflow.models.taskinstance import Context, TaskInstance, clear_task_instances
from airflow.models.taskmixin import TaskMixin
from airflow.models.xcom import XCOM_RETURN_KEY
from airflow.ti_deps.deps.base_ti_dep import BaseTIDep
from airflow.ti_deps.deps.not_in_retry_period_dep import NotInRetryPeriodDep
from airflow.ti_deps.deps.not_previously_skipped_dep import NotPreviouslySkippedDep
from airflow.ti_deps.deps.prev_dagrun_dep import PrevDagrunDep
from airflow.ti_deps.deps.trigger_rule_dep import TriggerRuleDep
from airflow.triggers.base import BaseTrigger
from airflow.utils import timezone
from airflow.utils.edgemodifier import EdgeModifier
from airflow.utils.helpers import validate_key
from airflow.utils.log.logging_mixin import LoggingMixin
from airflow.utils.operator_resources import Resources
from airflow.utils.session import NEW_SESSION, provide_session
from airflow.utils.trigger_rule import TriggerRule
from airflow.utils.weight_rule import WeightRule
if TYPE_CHECKING:
    from airflow.models.dag import DAG
    from airflow.models.xcom_arg import XComArg
    from airflow.utils.task_group import TaskGroup
ScheduleInterval = Union[str, timedelta, relativedelta]
TaskStateChangeCallback = Callable[[Context], None]
TaskPreExecuteHook = Callable[[Context], None]
TaskPostExecuteHook = Callable[[Context, Any], None]
T = TypeVar('T', bound=FunctionType)
class BaseOperatorMeta(abc.ABCMeta):