Google is migrating the Contacts API to the new People API beginning in June 2021. In some of my Google Apps Scripts I use the ContactsApp class from the Contacts Service (https://developers.google.com/apps-script/reference/contacts). Will this service still will work after the migration to the new People API?
Apps Script acts as a client to the Contacts API and will receive the same error rates as all other clients.
After the sunset of Contacts API, any errors that would be returned when trying to use it will be seen no matter how it is called - be that a client library, the Apps Script wrapper, or just HTTP requests.
Google sent out an email recently informing of the change - and this should have been received regardless of whether they are using Contacts API directly, or have Apps Script projects which use it.
At the moment it doesn't seem that there are any plans for a PeopleService or equivalent - but the Apps Script Advanced Services do have People API integration.
I would also urge you to make a feature request for a PeopleService equivalent of ContactsService, if you would like to see something like this implemented. You can file a feature request for this here on Google's Issue Tracker under the Apps Script Feature Request component.