### 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)

dag = get_airflow_app().dag_bag.get_dag(dag_id)
            if dag:
                ti.task = dag.get_task(ti.task_id)
            if response_format == "json":
                logs, metadata = task_log_reader.read_log_chunks(ti, try_number, metadata)
                message = logs[0] if try_number is not None else logs
                return {"message": message, "metadata": metadata}
            metadata["download_logs"] = True
            attachment_filename = task_log_reader.render_log_filename(ti, try_number, session=session)
            log_stream = task_log_reader.read_log_stream(ti, try_number, metadata)
            return Response(
                response=log_stream,
                mimetype="text/plain",
                headers={"Content-Disposition": f"attachment; filename={attachment_filename}"},
            )
        except AttributeError as e:
            error_messages = [f"Task log handler does not support read logs.\n{e}\n"]
            metadata["end_of_log"] = True
            return {"message": error_messages, "error": True, "metadata": metadata}
    @expose("/log")
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_INSTANCE),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_LOG),
        ]
    )
    @action_logging
    @provide_session
    def log(self, session: Session = NEW_SESSION):