fix: [cherrypick][V12.3.0] patch profile-sync-controller storage entr…

…y path hash (#27219)

## **Description**

Patches the underlying `@metamask/profile-sync-controller` to use the
original storage key path for notifications.

This was merged in develop here
#27224

This fixes a critical issue where we were not using the same UserStorage
hashed entry. See release library changelog

https://github.com/MetaMask/core/blob/main/packages/profile-sync-controller/CHANGELOG.md#fixed

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## **Related issues**

Fixes:

## **Manual testing steps**

Test notifications flow, are notifications still working

## **Screenshots/Recordings**

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## **Pre-merge author checklist**

- [x] I've followed [MetaMask Contributor
Docs](https://github.com/MetaMask/contributor-docs) and [MetaMask
Extension Coding
Standards](https://github.com/MetaMask/metamask-extension/blob/develop/.github/guidelines/CODING_GUIDELINES.md).
- [x] I've completed the PR template to the best of my ability
- [x] I’ve included tests if applicable
- [x] I’ve documented my code using [JSDoc](https://jsdoc.app/) format
if applicable
- [x] I’ve applied the right labels on the PR (see [labeling
guidelines](https://github.com/MetaMask/metamask-extension/blob/develop/.github/guidelines/LABELING_GUIDELINES.md)).
Not required for external contributors.

## **Pre-merge reviewer checklist**

- [ ] I've manually tested the PR (e.g. pull and build branch, run the
app, test code being changed).
- [ ] I confirm that this PR addresses all acceptance criteria described
in the ticket it closes and includes the necessary testing evidence such
as recordings and or screenshots.