Adds the latest version of `@metamask/controllers`, and updates our usage of the `ApprovalController`, which has been migrated to `BaseControllerV2`. Of [the new `controllers` release](https://github.com/MetaMask/controllers/releases/tag/v15.0.0), only the `ApprovalController` migration should be breaking.
This is the first time we use events on the `ControllerMessenger` to update the badge, so I turned the messenger into a property on the main `MetaMaskController` in order to subscribe to events on it in `background.js`. I confirmed that the badge does indeed update during local QA.
As it turns out, [MetaMask/controllers#571](https://github.com/MetaMask/controllers/pull/571) was breaking for a single unit test case, which is now handled during setup and teardown for the related test suite (`metamask-controller.test.js`).