We've discovered that old token with the Google Contacts scope https://www.google.com/m8/feeds/ can be used to access Google People API to access user' contacts. Migration guide provided by Google explains what new scopes Google People API needs, but doesn't explain whether the old token can be kept (https://developers.google.com/people/contacts-api-migration).
Keeping the old token is the preferred option because it doesn't require user interaction (user doesn't have to re-authorize his/her Google account on our system).
According to Google - on December 15th - 100% of Contacts API requests will return an error, but what will happen if requests are made to Google People API, but with the Google Contacts access scope?
It will work for reading and writing contacts and contact groups, but not "Other contacts" or directory data. See https://developers.google.com/people/contacts-api-migration#scope_migration