Avoid recreating vault when changing password

### What is this about?

The "change password" feature currently recreates the entire vault. Recreating the vault correctly is quite complex so this is an error-prone process, and the deletion of the old vault might result in state loss for related state in other controllers.

We should use the `changePassword` method instead, which was added to allow changing password without destroying the vault (https://github.com/MetaMask/core/pull/4279). This would let us eliminate some complex error-prone code, and avoid any risk of state loss from keyrings being deleted.

### Scenario

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### Design

_No response_

### Technical Details

Here is the relevant code: https://github.com/MetaMask/metamask-mobile/blob/6e9b68821a02c40cf9cbd3bb844d6168b72a03d1/app/core/Vault.js#L56

### Threat Modeling Framework

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### Acceptance Criteria

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### Stakeholder review needed before the work gets merged

- [x] Engineering (needed in most cases)
- [ ] Design
- [ ] Product
- [ ] QA (automation tests are required to pass before merging PRs but not all changes are covered by automation tests - please review if QA is needed beyond automation tests)
- [ ] Security
- [ ] Legal
- [ ] Marketing
- [ ] Management (please specify)
- [ ] Other (please specify)

### References

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Begin at app/core/Vault.js around line 56 and compare the current password-change flow with core's changePassword method from PR #4279. Done means changing the password no longer recreates or deletes the vault, avoiding potential keyring state loss; verify the applicable Vault behavior afterward.

Written by the indexing model from the issue text.