Refactor BroadcastMessage to use Gitlab::JsonCache

What does this MR do?

Refactor the BroadcastMessage model to use the Gitlab::JsonCache introduce in https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/8802.

What are the relevant issue numbers?

https://gitlab.com/gitlab-org/gitlab-ce/issues/55034

Does this MR meet the acceptance criteria?

• ~~~Changelog entry added, if necessary~~
• Documentation created/updated
• Tests added for this feature/bug
• Tested in all supported browsers
• Conforms to the code review guidelines
• Conforms to the merge request performance guidelines
• Conforms to the style guides
• Conforms to the database guides
• Link to e2e tests MR added if this MR has Requires e2e tests label. See the Test Planning Process.
• Security reports checked/validated by reviewer