feat: Add MetaMetrics event for "Use different login method" click during social login rehydration (#37349)

## **Description**

This PR adds MetaMetrics tracking for when users click the "Use a
different login method" button during social login rehydration flow

**What is the reason for the change?**
We need to track when users decide to switch login methods during the
rehydration phase

**What is the improvement/solution?**
Added a new MetaMetrics event `UseDifferentLoginMethodClicked` that
fires when:
- User is in social login flow
- Onboarding is not completed (rehydration phase)
- User clicks "Use a different login method" on the welcome back screen

[![Open in GitHub
Codespaces](https://github.com/codespaces/badge.svg)](https://codespaces.new/MetaMask/metamask-extension/pull/37349?quickstart=1)

## **Changelog**

CHANGELOG entry: null

## **Related issues**

Fixes: https://consensyssoftware.atlassian.net/browse/SL-241

## **Manual testing steps**

1. Start a social login import flow (Google or Apple)
2. Complete authentication with the provider
3. Navigate to the unlock/rehydration screen (welcome back screen)
4. Click "Use a different login method" button
5. Verify the `UseDifferentLoginMethodClicked` event is tracked with
`account_type: 'social'`

## **Screenshots/Recordings**

### **Before**
No MetaMetrics event tracked when clicking "Use a different login
method" during rehydration

### **After**
`UseDifferentLoginMethodClicked` event tracked with proper account_type
property

## **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/main/.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/main/.github/guidelines/LABELING_GUIDELINES.md)).
Not required for external contributors.

## **Pre-merge reviewer checklist**

- [x] I've manually tested the PR (e.g. pull and build branch, run the
app, test code being changed).
- [x] 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.


<!-- CURSOR_SUMMARY -->
---

> [!NOTE]
> Adds a new MetaMetrics event and tracking on the unlock page for
clicks to use a different login method during social login rehydration.
> 
> - **Analytics (MetaMetrics)**:
> - Add `UseDifferentLoginMethodClicked` to `MetaMetricsEventName` in
`shared/constants/metametrics.ts`.
> - **UI**:
> - Track `UseDifferentLoginMethodClicked` in
`ui/pages/unlock-page/unlock-page.component.js` when in social login
rehydration (onboarding not completed) before redirecting to
`onboarding_welcome`, with `properties.account_type = 'social'`.
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
96edf3a. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

Author: huggingbot

shared/constants/metametrics.ts

@@ -842,6 +842,7 @@ export enum MetaMetricsEventName {
   RehydrationPasswordAttempted = 'Rehydration Password Attempted',
   RehydrationCompleted = 'Rehydration Completed',
   RehydrationPasswordFailed = 'Rehydration Password Failed',
+  UseDifferentLoginMethodClicked = 'Use Different Login Method Clicked',
   // BEGIN:ONLY_INCLUDE_IF(build-flask,build-experimental)
   WatchEthereumAccountsToggled = 'Watch Ethereum Accounts Toggled',
   // END:ONLY_INCLUDE_IF

ui/pages/unlock-page/unlock-page.component.js

@@ -391,6 +391,15 @@ class UnlockPage extends Component {
     // in `onboarding_unlock` route, if the user is on a social login flow and onboarding is not completed,
     // we can redirect to `onboarding_welcome` route to select a different login method
     if (!isOnboardingCompleted && isSocialLoginFlow) {
+      // Track when user clicks "Use a different login method" during rehydration
+      this.context.trackEvent({
+        category: MetaMetricsEventCategory.Onboarding,
+        event: MetaMetricsEventName.UseDifferentLoginMethodClicked,
+        properties: {
+          account_type: 'social',
+        },
+      });
+
       await this.props.loginWithDifferentMethod();
       await this.props.forceUpdateMetamaskState();
       history.replace(ONBOARDING_WELCOME_ROUTE);