### 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)

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                segments = table_name.split("__", 3)
                if len(segments) < 3:
                    continue
                if segments[0] != settings.AIRFLOW_MOVED_TABLE_PREFIX:
                    continue
                
                yield segments[-1], table_name
        if (
            permissions.ACTION_CAN_ACCESS_MENU,
            permissions.RESOURCE_ADMIN_MENU,
        ) in user_permissions and conf.getboolean("webserver", "warn_deployment_exposure"):
            robots_file_access_count = (
                select(Log)
                .where(Log.event == "robots")
                .where(Log.dttm > (utcnow() - datetime.timedelta(days=7)))
            )
            robots_file_access_count = get_query_count(robots_file_access_count, session=session)
            if robots_file_access_count > 0:
                flash(
                    Markup(
                        "Recent requests have been made to /robots.txt. "
                        "This indicates that this deployment may be accessible to the public internet. "
                        "This warning can be disabled by setting webserver.warn_deployment_exposure=False in "
                        "airflow.cfg. Read more about web deployment security <a href="
                        f'"{get_docs_url("security/webserver.html")}">'