### Apache Airflow version

2.7.0

### What happened

On the DAGs page, the All, Active, and Paused counts include deleted DAGs. This is different from <= 2.6.1 (at least), where they were not included in the totals. Specifically this is for DAGs for which the DAG files have been removed, not DAGs that have been deleted via the UI.

### What you think should happen instead

Including deleted DAGs in those counts is confusing, and this behavior should revert to the previous behavior.

### How to reproduce

Create a DAG. 
Wait for totals to increment.
Remove the DAG file.

The totals will not change.

### Operating System

Debian GNU/Linux 11 (bullseye)

### Versions of Apache Airflow Providers

```apache-airflow-providers-amazon==8.5.1
apache-airflow-providers-celery==3.3.2
apache-airflow-providers-cncf-kubernetes==7.4.2
apache-airflow-providers-common-sql==1.7.0
apache-airflow-providers-datadog==3.3.1
apache-airflow-providers-elasticsearch==5.0.0
apache-airflow-providers-ftp==3.5.0
apache-airflow-providers-google==10.6.0
apache-airflow-providers-http==4.5.0
apache-airflow-providers-imap==3.3.0
apache-airflow-providers-microsoft-azure==6.2.4
apache-airflow-providers-postgres==5.6.0
apache-airflow-providers-redis==3.3.1
apache-airflow-providers-salesforce==5.4.1
apache-airflow-providers-slack==7.3.2
apache-airflow-providers-snowflake==4.4.2
apache-airflow-providers-sqlite==3.4.3
```

### Deployment

Astronomer

### Deployment details

_No response_

### Anything else

I suspect the issue is with [DagModel.deactivate_deleted_dags](https://github.com/apache/airflow/blob/f971ba2f2f9703d0e1954e52aaded52a83c2f844/airflow/models/dag.py#L3564), but I'm unable to verify.



### 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)

no_dagrun = True
        else:
            ti = dag_run.get_task_instance(task_id=task_id, map_index=map_index, session=session)
            if ti:
                ti.refresh_from_task(raw_task)
            else:
                flash(f"there is no task instance with the provided map_index {map_index}", "error")
                return self.render_template(
                    "airflow/ti_code.html",
                    show_trigger_form_if_no_params=conf.getboolean(
                        "webserver", "show_trigger_form_if_no_params"
                    ),
                    html_dict=html_dict,
                    dag=dag,
                    task_id=task_id,
                    execution_date=execution_date,
                    map_index=map_index,
                    form=form,
                    root=root,
                    title=title,
                )
        try:
            ti.get_rendered_template_fields(session=session)
        except AirflowException as e:
            if not e.__cause__:
                flash(f"Error rendering template: {e}", "error")
            else:
                msg = Markup("Error rendering template: {0}<br><br>OriginalError: {0.__cause__}").format(e)
                flash(msg, "error")
        except Exception as e: