RRM connect page doesn't reload when returning from publisher centre

## Bug Description

I noticed this scenario which isn't quite what it used to be like.
Here's the scenario
- I set up RRM and I am directed to RRM website to create the publication
- After after I create the publication and go back to SK, previously, it would auto-reload to fetch the publication but right now, this auto-reload doesn't happen anymore.
- Refer to the video at around 1m 30 seconds.

https://github.com/user-attachments/assets/c03931fd-a1be-4350-b3ed-4ce1ab9bc826

## Steps to reproduce

1. Go to '...'
2. Click on '....'
3. Scroll down to '....'
4. See error

## Screenshots

## Additional Context

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

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## Acceptance criteria

*

## Implementation Brief

* [ ]

### Test Coverage

*

## QA Brief

*

## Changelog entry

*

Start by reproducing the RRM setup flow, returning from the publisher centre to the Site Kit connection page, and observe whether the publication is fetched. Trace the return handling for that page; done means the page automatically reloads and displays the newly created publication.

Written by the indexing model from the issue text.