Delayed Success Notice When Enabling Groups in Settings on Dev Environment.

## Bug Description

On the dev environment, under settings, when enabling groups, the success notice appears after a few seconds’ delay. I verified the same on the latest environment, and this issue is not reproducible there, so it seems to be a regression.

## Steps to reproduce

1. Setup Site Kit.
2. Go to Site Kit > Settings > Admin Settings > Visitor click on Enable visitor groups, Once setup setup success notification will be shown.

## Screenshots

**Latest:**

https://github.com/user-attachments/assets/c25ecebb-cfff-4192-a005-1b42b7712d17

**Dev :**

https://github.com/user-attachments/assets/1c5b87ab-727b-4183-823f-a66abc288917

https://github.com/user-attachments/assets/7b0f66fc-e890-4e66-bf03-97e1aa8e5cda

## Additional Context

- PHP Version:
- OS: [e.g. iOS]
- Browser: [e.g. chrome, safari]
- Plugin Version: [e.g. 22]
- Device: [e.g. iPhone6]

---------------

_Do not alter or remove anything below. The following sections will be managed by moderators only._

## Acceptance criteria

*

## Implementation Brief

* [ ]

### Test Coverage

*

## QA Brief

*

## Changelog entry

*

Reproduce the issue through Site Kit > Settings > Admin Settings > Visitor on the dev environment, comparing it with the latest environment and the provided screenshots. Trace when the success notification appears after enabling visitor groups. Done means the dev environment shows the success notice without the reported delay and the behavior remains correct in the latest environment.

Written by the indexing model from the issue text.