Migrate branch switcher to Vue

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Currently, the branch switcher cannot easily communicate with the rest of the app to maintain state. Moving to Vue will allow the switcher to keep track of the currently selected path when opening directories in the file viewer.

The following discussion from !46479 (merged) should be addressed:

• @jboyson started a discussion: (+1 comment)

  This is not the final solution to this problem, just a stop-gap until we can refactor this away from jQuery and haml