### 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)

category="error",
                )
                del form.extra
        del extra_json
        for key, field_name, is_sensitive in self._iter_extra_field_names_and_sensitivity():
            if key in form.data and key.startswith("extra__"):
                conn_type_from_extra_field = key.split("__")[1]
                if conn_type_from_extra_field == conn_type:
                    value = form.data[key]
                    
                    
                    if value != "":
                        extra[field_name] = value
        if extra.keys():
            sensitive_unchanged_keys = set()
            for key, value in extra.items():
                if value == SENSITIVE_FIELD_PLACEHOLDER:
                    sensitive_unchanged_keys.add(key)
            if sensitive_unchanged_keys:
                try:
                    conn = BaseHook.get_connection(conn_id)
                except AirflowNotFoundException:
                    conn = None
                for key in sensitive_unchanged_keys:
                    if conn and conn.extra_dejson.get(key):
                        extra[key] = conn.extra_dejson.get(key)
                    else:
                        del extra[key]
            form.extra.data = json.dumps(extra)
    def prefill_form(self, form, pk):