### 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)

group_state = next((state for state in wwwutils.priority if state in children_states), None)
                group_queued_dttm = min(filter(None, children_queued_dttms), default=None)
                group_start_date = min(filter(None, children_start_dates), default=None)
                group_end_date = max(filter(None, children_end_dates), default=None)
                return {
                    "task_id": task_group.group_id,
                    "run_id": run_id,
                    "state": group_state,
                    "queued_dttm": group_queued_dttm,
                    "start_date": group_start_date,
                    "end_date": group_end_date,
                    "mapped_states": mapped_states,
                }
            return [get_mapped_group_summary(run_id, tis) for run_id, tis in mapped_tis.items()]
        
        if task_group.group_id is None:
            return {
                "id": task_group.group_id,
                "label": task_group.label,
                "children": children,
                "instances": [],
            }
        if group_is_mapped:
            mapped_group_summaries = get_mapped_group_summaries()
            return {
                "id": task_group.group_id,
                "label": task_group.label,
                "children": children,
                "tooltip": task_group.tooltip,
                "instances": mapped_group_summaries,