Log in as admin.
Click on Discussion 1 SMPL101 (any site with Lessons will do)
In Lessons, click Add Content
Choose "Embed Announcements" (beforehand make certain there is at least one announcement)
Verify your user preferences: English (US) and US/East time zone were mine.
Announcements itself displays times correctly: June 29, 2018 3:24pm
Result: The Announcement tool displays the time in 24 hr format. Is this a server-setting or a bug?