### 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)

"unless:<br>\n- The scheduler is down or under heavy load<br>\n{}\n"
                "<br>\nIf this task instance does not start soon please contact your "
                "Airflow administrator for assistance.".format(
                    "- This task instance already ran and had it's state changed manually "
                    "(e.g. cleared in the UI)<br>"
                    if ti and ti.state is None
                    else ""
                ),
            )
        ]
        
        if ti is None:
            failed_dep_reasons: list[tuple[str, str]] = []
        else:
            dep_context = DepContext(SCHEDULER_QUEUED_DEPS)
            failed_dep_reasons = [
                (dep.dep_name, dep.reason) for dep in ti.get_failed_dep_statuses(dep_context=dep_context)
            ]
        title = "Task Instance Details"
        return self.render_template(
            "airflow/task.html",
            show_trigger_form_if_no_params=conf.getboolean("webserver", "show_trigger_form_if_no_params"),
            task_attrs=task_attrs,
            ti_attrs=ti_attrs,
            failed_dep_reasons=failed_dep_reasons or no_failed_deps_result,
            task_id=task_id,
            execution_date=execution_date,
            map_index=map_index,
            special_attrs_rendered=special_attrs_rendered,
            form=form,