Flickering issue before AdSense High potential notification appears.

## Bug Description

There is flickering when other notifications also exist. Upon page load, the "Gathering data" notification appears first, followed by the "Connect EM" notification, and finally, the AdSense HP notification appears. Can we prevent flickering in this case and prioritize displaying the notification with the highest priority upon load?

## Steps to reproduce

1. Set up SK on new site having zero or gathering data state.
2. Make sure site is added into eligible site list.
3. Visit site dashboard.
4. Notice that upon page load, the "Gathering data" notification appears first, followed by the AdSense Alert notification.

## Screenshots

https://github.com/user-attachments/assets/066121f1-acc4-4d2f-abde-dd11ec16d5bb

Old Screen Recording
https://github.com/google/site-kit-wp/assets/94359491/10a94829-5b60-4d6d-be15-098d57db57f4

## 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

* Core Site Banner Notifications and AdSense alerts should appear before Gathering Data / Zero Data state Banner Notifications and there should be no "flicker" or change of notifications once one is rendered.

## Implementation Brief

* [ ]

### Test Coverage

*

## QA Brief

*

## Changelog entry

*