### Apache Airflow version

2.1.3

### Operating System

Debian GNU/Linux 9 (stretch)

### Versions of Apache Airflow Providers

_No response_

### Deployment

Other Docker-based deployment

### Deployment details

_No response_

### What happened

In the DAG tree view, if I select a custom date in the date filter (top left corner) and press "update", DAG runs are correctly filtered to the selected date and number of runs.
 
However, if the "auto-refresh" toggle is on, when the next tick refresh happens, the date filter is no longer taken into account and the UI displays the actual **latest** x DAG runs status. However, neither the header dates (45° angle) nor the date filter reflect this new time window 

I investigated in the network inspector and it seems that the xhr request that fetches dag runs status doesn't contain a date parameter and thus always fetch the latest DAG run data

### What you expected to happen

I expect that the auto-refresh feature preserves the selected time window

### How to reproduce

Open a DAG with at least 20 dag runs
Make sure autorefresh is disabled
Select a filter date earlier than the 10th dag run start date and a "number of runs" value of 10, press "update"
The DAG tree view should now be focused on the 10 first dag runs
Now toggle autorefresh and wait for next tick
The DAG tree view will now display status of the latest 10 runs but the header dates will still reflect the old start dates

### Anything else

_No response_

### Are you willing to submit PR?

- [X] 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)

airflow/www/views.py
from airflow.jobs.base_job import BaseJob
from airflow.jobs.scheduler_job import SchedulerJob
from airflow.jobs.triggerer_job import TriggererJob
from airflow.models import DAG, Connection, DagModel, DagTag, Log, SlaMiss, TaskFail, XCom, errors
from airflow.models.baseoperator import BaseOperator
from airflow.models.dagcode import DagCode
from airflow.models.dagrun import DagRun, DagRunType
from airflow.models.serialized_dag import SerializedDagModel
from airflow.models.taskinstance import TaskInstance
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 RUNNING_DEPS, SCHEDULER_QUEUED_DEPS
from airflow.utils import json as utils_json, timezone, yaml
from airflow.utils.dates import infer_time_unit, scale_time_units
from airflow.utils.docs import get_doc_url_for_provider, get_docs_url
from airflow.utils.helpers import alchemy_to_dict
from airflow.utils.log import secrets_masker
from airflow.utils.log.log_reader import TaskLogReader
from airflow.utils.session import create_session, provide_session
from airflow.utils.state import State
from airflow.utils.strings import to_boolean
from airflow.version import version
from airflow.www import auth, utils as wwwutils
from airflow.www.decorators import action_logging, gzipped
from airflow.www.forms import (
    ConnectionForm,
    DagRunEditForm,
    DateTimeForm,
    DateTimeWithNumRunsForm,