Proton does not currently offer CalDAV or CardDAV services, however there is a highly modular platform used by many large companies that allows for simple integration into third party authentication services: Baikal, backed by sabre/dav.
Does Proton have a published API that could be leveraged for authentication? sabre/dav already has a plugin for IMAP, but of course that can’t put targeted to Proton. Many services offer access to their IDP these days, I’m wondering if there is a service like this from Proton as well?
Proto calendar does have an ics thing. Maybe you can use drive to backup your contacts