Auto-refresh and DAG double-trigger issues when toggling pause

### Apache Airflow version

2.7.2

### What happened

Problems that I discovered: 1) If DAG is on pause, then when you go into it and unpause it with the button on the left, the DAG trigger turns on, but auto-update does not turn on 2) if DAG is on pause, and you turn it on with the play button (on the right ), then the dag is launched twice - as if once due to the inclusion of the dag and the second due to the activation of an already enabled dag

### What you think should happen instead

After unpause DAG button auto-update should be turned on (the same behavior like after clear task)

After push play button DAG should be triggered only one time

### How to reproduce

## Steps to Reproduce

1. Have a DAG on pause.
2. Navigate to the DAG's page in the Airflow UI.
3. Toggle the pause off using the trigger DAG button on the left.
4. Observe that the DAG is resumed but auto-refresh is not enabled.
5. Now, toggle the pause off using the play button on the right.
6. Observe that the DAG is triggered twice, seemingly once for the un-pausing and once for the activation of the already resumed DAG.

### Operating System

Linux from docker, and linux (rhel)

### Versions of Apache Airflow Providers

_No response_

### Deployment

Virtualenv installation

### Deployment details

I think it's doesn't connected with deployment.
I have the same problems in 2 different envs and also with airflow more earlier versions

### 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)

Start by reproducing the two behaviors in the Airflow UI using the listed pause, trigger, and play-button steps. Trace the UI actions involved in unpausing and triggering a DAG, then verify that unpausing enables auto-refresh and that the play-button flow creates only one trigger.

Written by the indexing model from the issue text.