Pick broadcast message colors from palette instead of hex color codes

Description

Back in 8.10.6, broadcast message background and font colors could be picked from a color palette. Today, users have to manually enter the color hex codes, which is unintuitive.

Proposal

Allow users to pick the colors they want from a color palette again.

Links / references

The way it was in 8.10.6:

The way it is now, in 8.16.4:

This was mentioned by an EE customer in https://gitlab.zendesk.com/agent/tickets/57659