### 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)

DagRun.data_interval_end,
            ).join(
                last_runs_subquery,
                and_(
                    last_runs_subquery.c.dag_id == DagRun.dag_id,
                    last_runs_subquery.c.max_execution_date == DagRun.execution_date,
                ),
            )
        )
        resp = {
            r.dag_id.replace(".", "__dot__"): {
                "dag_id": r.dag_id,
                "state": r.state,
                "execution_date": wwwutils.datetime_to_string(r.execution_date),
                "start_date": wwwutils.datetime_to_string(r.start_date),
                "end_date": wwwutils.datetime_to_string(r.end_date),
                "data_interval_start": wwwutils.datetime_to_string(r.data_interval_start),
                "data_interval_end": wwwutils.datetime_to_string(r.data_interval_end),
            }
            for r in query
        }
        return flask.json.jsonify(resp)
    @expose("/code")
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG_CODE),
        ]
    )
    def legacy_code(self):