### 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)

from airflow.utils.log import secrets_masker
from airflow.utils.log.log_reader import TaskLogReader
from airflow.utils.net import get_hostname
from airflow.utils.session import NEW_SESSION, create_session, provide_session
from airflow.utils.state import DagRunState, State, TaskInstanceState
from airflow.utils.strings import to_boolean
from airflow.utils.task_group import MappedTaskGroup, TaskGroup, task_group_to_dict
from airflow.utils.timezone import td_format, utcnow
from airflow.version import version
from airflow.www import auth, utils as wwwutils
from airflow.www.decorators import action_logging, gzipped
from airflow.www.extensions.init_auth_manager import get_auth_manager
from airflow.www.forms import (
    DagRunEditForm,
    DateTimeForm,
    DateTimeWithNumRunsForm,
    TaskInstanceEditForm,
    create_connection_form_class,
)
from airflow.www.widgets import AirflowModelListWidget, AirflowVariableShowWidget
PAGE_SIZE = conf.getint("webserver", "page_size")
FILTER_TAGS_COOKIE = "tags_filter"
FILTER_STATUS_COOKIE = "dag_status_filter"
LINECHART_X_AXIS_TICKFORMAT = (
    "function (d, i) { let xLabel;"
    "if (i === undefined) {xLabel = d3.time.format('%H:%M, %d %b %Y')(new Date(parseInt(d)));"
    "} else {xLabel = d3.time.format('%H:%M, %d %b')(new Date(parseInt(d)));} return xLabel;}"
)
SENSITIVE_FIELD_PLACEHOLDER = "RATHER_LONG_SENSITIVE_FIELD_PLACEHOLDER"
def sanitize_args(args: dict[str, str]) -> dict[str, str]: