Upgrade @metamask/bridge-controller to version 78.0.0

A new major version of `@metamask/bridge-controller`, 78.0.0, is now available. This issue has been assigned to you and your team because you code-own this package in the `core` repo. If this package is present in this project, please prioritize upgrading it soon to unblock new features and bugfixes.

Start by locating the dependency declaration for @metamask/bridge-controller in the metamask-extension repository and checking how dependency upgrades are verified. Update it to version 78.0.0, then run the repository's relevant checks; done means the project uses the requested version without introducing failures.

Written by the indexing model from the issue text.