### 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
self,
        task_id: str,
        owner: str = conf.get('operators', 'DEFAULT_OWNER'),
        email: Optional[Union[str, Iterable[str]]] = None,
        email_on_retry: bool = conf.getboolean('email', 'default_email_on_retry', fallback=True),
        email_on_failure: bool = conf.getboolean('email', 'default_email_on_failure', fallback=True),
        retries: Optional[int] = conf.getint('core', 'default_task_retries', fallback=0),
        retry_delay: Union[timedelta, float] = timedelta(seconds=300),
        retry_exponential_backoff: bool = False,
        max_retry_delay: Optional[Union[timedelta, float]] = None,
        start_date: Optional[datetime] = None,
        end_date: Optional[datetime] = None,
        depends_on_past: bool = False,
        wait_for_downstream: bool = False,
        dag: Optional['DAG'] = None,
        params: Optional[Dict] = None,
        default_args: Optional[Dict] = None,
        priority_weight: int = 1,
        weight_rule: str = conf.get('core', 'default_task_weight_rule', fallback=WeightRule.DOWNSTREAM),
        queue: str = conf.get('operators', 'default_queue'),
        pool: Optional[str] = None,
        pool_slots: int = 1,
        sla: Optional[timedelta] = None,
        execution_timeout: Optional[timedelta] = None,
        on_execute_callback: Optional[TaskStateChangeCallback] = None,
        on_failure_callback: Optional[TaskStateChangeCallback] = None,
        on_success_callback: Optional[TaskStateChangeCallback] = None,
        on_retry_callback: Optional[TaskStateChangeCallback] = None,
        pre_execute: Optional[TaskPreExecuteHook] = None,
        post_execute: Optional[TaskPostExecuteHook] = None,