I guess you just create a new tab, then have a table for admins to write announcements to. On posting a new row to the Announcements table, trigger your Zap to send out notifications, but beware of the number of email addresses you can send to in a single email to not go over the quota.
Getting a true pop-up is a bit of a hack with Glide Apps, and not available with Glide Pages. If you want to dive into it with CSS, read this.
Looks like it can be done as an inline list, and you make the right filter to show only the newest notifications/unread notifications. Use a user-specific column to determine whether the user has read the announcement or not, once they click on it, set the column to true.