You mark an appointment Private and assume only you can read its details. In a shared Google Calendar, that depends on the viewer's permissions. Check both the event setting and who has access to the calendar.
Read the full permission name
On a computer, open the calendar's Settings and sharing and review the people, groups and wider access settings. Google's current documentation distinguishes editing with private events shown only as free/busy from editing with permission to see event details. The latter, and the role that can manage sharing, can see private event details. “Can edit” alone is therefore too vague to describe the arrangement.
For the restricted editing role, a private event marked Busy appears as a block without details; one marked Free is absent from the calendar grid. Work or school administrators can also have special access. Check the rules for that account rather than assuming a personal-calendar setup applies.
Test a harmless event, not a real appointment
Create a separate test event with an ordinary title and no guests or room booking. Set its visibility to Private, then ask a trusted calendar viewer with the intended permission to describe what they see. Test the access level you actually plan to use, not an owner's view.
Inviting guests or booking a room creates additional visibility considerations: Google notes that even private events can expose some details, such as times and the creator. Keep unnecessary descriptions and attachments out of a simple availability block. If you edit a recurring event's visibility, Google says the change applies to the entire series. Review the scope before saving, and revisit sharing when the group changes.