### 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)

form_fields[k]["schema"]["type"] = ["object", "null"]
            
            if (
                "description_html" in form_fields[k]["schema"]
                and form_fields[k]["schema"]["description_html"]
            ):
                form_fields[k]["description"] = Markup(form_fields[k]["schema"]["description_html"])
            if "custom_html_form" in form_fields[k]["schema"]:
                form_fields[k]["schema"]["custom_html_form"] = Markup(
                    form_fields[k]["schema"]["custom_html_form"]
                )
        ui_fields_defined = any("const" not in f["schema"] for f in form_fields.values())
        show_trigger_form_if_no_params = conf.getboolean("webserver", "show_trigger_form_if_no_params")
        if not dag_orm:
            flash(f"Cannot find dag {dag_id}")
            return redirect(origin)
        if dag_orm.has_import_errors:
            flash(f"Cannot create dagruns because the dag {dag_id} has import errors", "error")
            return redirect(origin)
        recent_runs = session.execute(
            select(DagRun.conf, func.max(DagRun.run_id).label("run_id"), func.max(DagRun.execution_date))
            .where(
                DagRun.dag_id == dag_id,
                DagRun.run_type == DagRunType.MANUAL,
                DagRun.conf.isnot(None),
            )
            .group_by(DagRun.conf)
            .order_by(func.max(DagRun.execution_date).desc())
            .limit(5)
        )