Convert broadcast messages table to Vue

What does this MR do and why?

Related issue #368847 (closed)

Builds off of the feature flag and skeleton added in !98127 (merged), and converts the broadcast messages table to Vue. The goal of this MR was to reach feature parity with the existing HAML UI, so improvements can be implemented in a future MR if necessary.

Screenshots or screen recordings

Feature disabled

Feature enabled

How to set up and validate locally

1. Enable the Vue app

   Feature.enable(:vue_broadcast_messages)

2. Navigate to the broadcast messages view: http://gdk.test:3000/admin/broadcast_messages

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.