refactor: use core profile syncing controllers. (#26370)

## **Description**

1st migration to shared controllers. This adds the reusable controllers
from core. Migrated `AuthenticationController` and
`UserStorageController`

[![Open in GitHub
Codespaces](https://github.com/codespaces/badge.svg)](https://codespaces.new/MetaMask/metamask-extension/pull/26370?quickstart=1)

## **Related issues**

Fixes: N/A

## **Manual testing steps**

1. Go to this page...
2.
3.

## **Screenshots/Recordings**

<!-- If applicable, add screenshots and/or recordings to visualize the
before and after of your change. -->

### **Before**

<!-- [screenshots/recordings] -->

### **After**

<!-- [screenshots/recordings] -->

## **Pre-merge author checklist**

- [ ] 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).
- [ ] I've completed the PR template to the best of my ability
- [ ] I’ve included tests if applicable
- [ ] I’ve documented my code using [JSDoc](https://jsdoc.app/) format
if applicable
- [ ] 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.

---------

Co-authored-by: MetaMask Bot <[email protected]>