### 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
new_cls = super().__new__(cls, name, bases, namespace, **kwargs)
        new_cls.__init__ = cls._apply_defaults(new_cls.__init__)
        return new_cls
@functools.total_ordering
class BaseOperator(Operator, LoggingMixin, TaskMixin, metaclass=BaseOperatorMeta):
    """
    Abstract base class for all operators. Since operators create objects that
    become nodes in the dag, BaseOperator contains many recursive methods for
    dag crawling behavior. To derive this class, you are expected to override
    the constructor as well as the 'execute' method.
    Operators derived from this class should perform or trigger certain tasks
    synchronously (wait for completion). Example of operators could be an
    operator that runs a Pig job (PigOperator), a sensor operator that
    waits for a partition to land in Hive (HiveSensorOperator), or one that
    moves data from Hive to MySQL (Hive2MySqlOperator). Instances of these
    operators (tasks) target specific operations, running specific scripts,
    functions or data transfers.
    This class is abstract and shouldn't be instantiated. Instantiating a
    class derived from this one results in the creation of a task object,
    which ultimately becomes a node in DAG objects. Task dependencies should
    be set by using the set_upstream and/or set_downstream methods.
    :param task_id: a unique, meaningful id for the task
    :type task_id: str
    :param owner: the owner of the task. Using a meaningful description
        (e.g. user/person/team/role name) to clarify ownership is recommended.
    :type owner: str
    :param email: the 'to' email address(es) used in email alerts. This can be a
        single email or multiple ones. Multiple addresses can be specified as a