### 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)

is_dag_run_conf_overrides_params=is_dag_run_conf_overrides_params,
                recent_confs=recent_confs,
            )
        try:
            execution_date = timezone.parse(request_execution_date, strict=True)
        except ParserError:
            flash("Invalid execution date", "error")
            form = DateTimeForm(data={"execution_date": timezone.utcnow().isoformat()})
            return self.render_template(
                "airflow/trigger.html",
                form_fields=form_fields,
                dag=dag,
                dag_id=dag_id,
                origin=origin,
                conf=request_conf if request_conf else {},
                form=form,
                is_dag_run_conf_overrides_params=is_dag_run_conf_overrides_params,
                recent_confs=recent_confs,
            )
        dr = DagRun.find_duplicate(dag_id=dag_id, run_id=run_id, execution_date=execution_date)
        if dr:
            if dr.run_id == run_id:
                message = f"The run ID {run_id} already exists"
            else:
                message = f"The logical date {execution_date} already exists"
            flash(message, "error")
            return redirect(origin)
        regex = conf.get("scheduler", "allowed_run_id_pattern")
        if run_id and not re2.match(RUN_ID_REGEX, run_id):
            if not regex.strip() or not re2.match(regex.strip(), run_id):