### 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)

return redirect_or_json(origin, msg)
        try:
            tis = dag.clear(
                start_date=start_date,
                end_date=end_date,
                task_ids=task_ids,
                include_subdags=recursive,
                include_parentdag=recursive,
                only_failed=only_failed,
                dry_run=True,
                session=session,
            )
        except AirflowException as ex:
            return redirect_or_json(origin, msg=str(ex), status="error", status_code=500)
        assert isinstance(tis, collections.abc.Iterable)
        details = [str(t) for t in tis]
        if not details:
            return redirect_or_json(origin, "No task instances to clear", status="error", status_code=404)
        elif request.headers.get("Accept") == "application/json":
            if confirmed:
                return htmlsafe_json_dumps(details, separators=(",", ":"))
            return htmlsafe_json_dumps(
                [{"task_id": ti.task_id, "map_index": ti.map_index, "run_id": ti.run_id} for ti in tis],
                separators=(",", ":"),
            )
        return self.render_template(
            "airflow/confirm.html",
            endpoint=None,
            message="Task instances you are about to clear:",
            details="\n".join(details),