We could provide an API endpoint that takes an email address and returns a few key data points like cid, most recent donation method, if they have a recurring donation or not, or whatever you like. We would have to consider what we do or don't want to include as far as PII, but I wouldn't assume we can't pass any from Civi to Zendesk. As above, the additional wrinkle here is that we may match more than one contact. We'd have to think through how we'd want this to work in that case.
Data returned to be determined in consultation with DR, but could include segment & status, most recent donations and methods, donor value to date, etc
This is a second step to be completed after T415378: Add link in Zendesk to contact in CiviCRM & unsubscribe form by email.