Before January 2019 — Google Calendar had an SMS notification option. It was part of Google Calendar's own notification system — a reminder sent to you through your Google account settings, not a client-reminder workflow for appointment businesses.
January 7, 2019 — Google removed SMS notifications from Google Calendar. Google said that people who had been receiving SMS notifications would instead get in-app/browser/mobile notifications and email notifications.
Since 2019 — Google Calendar still has notifications, but the current supported notification types are delivered on your phone, in your web browser, or by email. Google also says notification settings are personal to your account and do not determine notifications for other people who have access to the calendar.