### 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
ti = create_task_instance(dag_id='dag', task_id='op', execution_date=timezone.datetime(2018, 1, 1))
        expected_url = (
            'http://localhost:8080/log?'
            'execution_date=2018-01-01T00%3A00%3A00%2B00%3A00'
            '&task_id=op'
            '&dag_id=dag'
        )
        assert ti.log_url == expected_url
    def test_mark_success_url(self, create_task_instance):
        now = pendulum.now('Europe/Brussels')
        ti = create_task_instance(dag_id='dag', task_id='op', execution_date=now)
        query = urllib.parse.parse_qs(
            urllib.parse.urlparse(ti.mark_success_url).query, keep_blank_values=True, strict_parsing=True
        )
        assert query['dag_id'][0] == 'dag'
        assert query['task_id'][0] == 'op'
        assert pendulum.parse(query['execution_date'][0]) == now
    def test_overwrite_params_with_dag_run_conf(self, create_task_instance):
        ti = create_task_instance()
        dag_run = ti.dag_run
        dag_run.conf = {"override": True}
        params = {"override": False}
        ti.overwrite_params_with_dag_run_conf(params, dag_run)
        assert params["override"] is True
    def test_overwrite_params_with_dag_run_none(self, create_task_instance):
        ti = create_task_instance()
        params = {"override": False}
        ti.overwrite_params_with_dag_run_conf(params, None)
        assert params["override"] is False
    def test_overwrite_params_with_dag_run_conf_none(self, create_task_instance):