A Google Calendar connection acts with the permissions of the Google account that approved it. Signing into your Overskill app does not by itself connect that person's calendar.
Workspace connections
A calendar connected in the workspace's Integrations belongs to that workspace. Multiple named connections can be stored. The app can use an explicitly named connection or an app-specific selection; otherwise it falls back to the workspace's default connected account.
When building for clients, name the intended account clearly and have the builder confirm which connection it uses before creating events. Test with a harmless event and check the actual calendar. Do not disconnect a working default account just to add another client.
Each app user connecting a calendar
The platform also has user-level integration connections, separate from workspace connections. Your app needs a connect flow and code that uses the signed-in user's connection. The user must approve Google's consent screen. A workspace connection alone does not set up this flow for all your users.
Ask the builder to explain the current flow and test with two different users and accounts before relying on it for bookings. Check what happens when a person has not connected a calendar; an app should not silently write their booking to an unrelated account.
Connected integration actions use workspace credits. Google's account policies and consent permissions still apply.