### 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)

ParamValidationError,
    RemovedInAirflow3Warning,
)
from airflow.executors.executor_loader import ExecutorLoader
from airflow.hooks.base import BaseHook
from airflow.jobs.job import Job
from airflow.jobs.scheduler_job_runner import SchedulerJobRunner
from airflow.jobs.triggerer_job_runner import TriggererJobRunner
from airflow.models import Connection, DagModel, DagTag, Log, SlaMiss, TaskFail, Trigger, XCom, errors
from airflow.models.abstractoperator import AbstractOperator
from airflow.models.dag import DAG, get_dataset_triggered_next_run_info
from airflow.models.dagrun import RUN_ID_REGEX, DagRun, DagRunType
from airflow.models.dataset import DagScheduleDatasetReference, DatasetDagRunQueue, DatasetEvent, DatasetModel
from airflow.models.mappedoperator import MappedOperator
from airflow.models.operator import Operator
from airflow.models.serialized_dag import SerializedDagModel
from airflow.models.taskinstance import TaskInstance, TaskInstanceNote
from airflow.providers_manager import ProvidersManager
from airflow.security import permissions
from airflow.ti_deps.dep_context import DepContext
from airflow.ti_deps.dependencies_deps import SCHEDULER_QUEUED_DEPS
from airflow.timetables._cron import CronMixin
from airflow.timetables.base import DataInterval, TimeRestriction
from airflow.utils import json as utils_json, timezone, yaml
from airflow.utils.airflow_flask_app import get_airflow_app
from airflow.utils.dag_edges import dag_edges
from airflow.utils.dates import infer_time_unit, scale_time_units
from airflow.utils.db import get_query_count
from airflow.utils.docs import get_doc_url_for_provider, get_docs_url
from airflow.utils.helpers import exactly_one