### Apache Airflow version

2.1.3 (latest released)

### Operating System

ubuntu, macos

### Versions of Apache Airflow Providers

apache-airflow-providers-amazon==1.4.0
apache-airflow-providers-ftp==1.1.0
apache-airflow-providers-http==1.1.1
apache-airflow-providers-imap==1.0.1
apache-airflow-providers-postgres==1.0.2
apache-airflow-providers-slack==4.0.0
apache-airflow-providers-sqlite==1.0.2

### Deployment

Virtualenv installation

### Deployment details

_No response_

### What happened

We are using TriggerDagRunOperator in the end of DAG to retrigger current DAG:

`TriggerDagRunOperator(task_id=‘trigger_task’, trigger_dag_id=‘current_dag’)`

Everything works fine, except we have missing duration in UI and ​warnings in scheduler :

`[2021-09-07 15:33:12,890] {dagrun.py:604} WARNING - Failed to record duration of <DagRun current_dag @ 2021-09-07 12:32:17.035471+00:00: manual__2021-09-07T12:32:16.956461+00:00, externally triggered: True>: start_date is not set.`

And in web UI we can't see duration in TreeView and DAG has no started and duration values. 


### What you expected to happen

Correct behaviour with start date and duration metrics in web UI.

### How to reproduce

```
import pendulum
import pytz
from airflow import DAG
from airflow.operators.dummy import DummyOperator
from airflow.operators.trigger_dagrun import TriggerDagRunOperator


with DAG(
        start_date=pendulum.datetime(year=2021, month=7, day=1).astimezone(pytz.utc),
        schedule_interval='@daily',
        default_args={},
        max_active_runs=1,
        dag_id='current_dag'
) as dag:

    step1 = DummyOperator(task_id='dummy_task')

    trigger_self = TriggerDagRunOperator(task_id='trigger_self', trigger_dag_id='current_dag')

    step1 >> trigger_self
```


`[2021-09-08 12:53:35,094] {dagrun.py:604} WARNING - Failed to record duration of <DagRun current_dag @ 2021-01-04 03:00:11+00:00: backfill__2021-01-04T03:00:11+00:00, externally triggered: False>: start_date is not set.`


### Anything else

_No response_

### 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)

airflow/api/common/experimental/trigger_dag.py
#
#
#
"""Triggering DAG runs APIs."""
import json
from datetime import datetime
from typing import List, Optional, Union
from airflow.exceptions import DagNotFound, DagRunAlreadyExists
from airflow.models import DagBag, DagModel, DagRun
from airflow.utils import timezone
from airflow.utils.state import State
from airflow.utils.types import DagRunType
def _trigger_dag(