### 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)

elif cookie_val:
            
            return redirect(url_for("Airflow.index", tags=cookie_val.split(",")))
        if arg_status_filter is None:
            cookie_val = flask_session.get(FILTER_STATUS_COOKIE)
            if cookie_val:
                arg_status_filter = cookie_val
            else:
                arg_status_filter = "active" if hide_paused_dags_by_default else "all"
                flask_session[FILTER_STATUS_COOKIE] = arg_status_filter
        else:
            status = arg_status_filter.strip().lower()
            flask_session[FILTER_STATUS_COOKIE] = status
            arg_status_filter = status
        dags_per_page = PAGE_SIZE
        start = current_page * dags_per_page
        end = start + dags_per_page
        
        filter_dag_ids = get_airflow_app().appbuilder.sm.get_accessible_dag_ids(g.user)
        with create_session() as session:
            
            dags_query = select(DagModel).where(~DagModel.is_subdag, DagModel.is_active)
            if arg_search_query:
                escaped_arg_search_query = arg_search_query.replace("_", r"\_")
                dags_query = dags_query.where(
                    DagModel.dag_id.ilike("%" + escaped_arg_search_query + "%", escape="\\")
                    | DagModel.owners.ilike("%" + escaped_arg_search_query + "%", escape="\\")
                )
            if arg_tags_filter:
                dags_query = dags_query.where(DagModel.tags.any(DagTag.name.in_(arg_tags_filter)))