### 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)

"""
    Prevents ability to pass primary keys of objects relating to DAGs you shouldn't be able to edit.
    This only holds for the add, update and delete operations.
    You will still need to use the `action_has_dag_edit_access()` for actions.
    """
    @staticmethod
    def validate_dag_edit_access(item: DagRun | TaskInstance):
        """Validates whether the user has 'can_edit' access for this specific DAG."""
        if not get_airflow_app().appbuilder.sm.can_edit_dag(item.dag_id):
            raise AirflowException(f"Access denied for dag_id {item.dag_id}")
    def pre_add(self, item: DagRun | TaskInstance):
        self.validate_dag_edit_access(item)
    def pre_update(self, item: DagRun | TaskInstance):
        self.validate_dag_edit_access(item)
    def pre_delete(self, item: DagRun | TaskInstance):
        self.validate_dag_edit_access(item)
    def post_add_redirect(self):  
        return redirect(self.get_default_url())
    def post_edit_redirect(self):  
        return redirect(self.get_default_url())
    def post_delete_redirect(self):