Move discussionTabCounter logic out of notes_app.vue component

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GitLab shows the total number of discussions in the Discussions tab on an Issue in EE. The DOM element that holds this number is currently being updates within the notes_app.vue component.

In !20899 (merged) @pslaughter noted that this approach could be improved in this discussion, specifically that:

It would be nice to move this whole functionality to somewhere like notes/index.js and just add a watcher on the store when it's created

This issue therefore encapsulates the work to move this logic out of this component into a spot that makes more sense (possibly notes/index.js), with the goal of reducing side-effects within Vue components (notes_app in this case)