### 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)

)
            .filter_by(execution_date=dttm, dag_id=dag_id, task_id=task_id, map_index=map_index)
        )
        if ti is None:
            ti_attrs: list[tuple[str, Any]] | None = None
        else:
            ti.refresh_from_task(task)
            ti_attrs_to_skip = [
                "dag_id",
                "key",
                "mark_success_url",
                "log",
                "log_url",
                "task",
                "trigger",
                "triggerer_job",
            ]
            
            with warnings.catch_warnings():
                warnings.simplefilter("ignore", RemovedInAirflow3Warning)
                all_ti_attrs = (
                    
                    (name, getattr(ti, "_try_number" if name == "try_number" else name))
                    for name in dir(ti)
                    if not name.startswith("_") and name not in ti_attrs_to_skip
                )
            ti_attrs = sorted((name, attr) for name, attr in all_ti_attrs if not callable(attr))
        attr_renderers = wwwutils.get_attr_renderer()
        attrs_to_skip: frozenset[str] = getattr(task, "HIDE_ATTRS_FROM_UI", frozenset())
        def include_task_attrs(attr_name):