I can confirm that the DAVx5 will synchronize both the contacts and the calendar (in my case, hosted at a Nextcloud instance) with the built-in Phone app and the Etar app, respectively.
Fun point: I ran synchronization of contacts and calendar in DAVx5 before I sideloaded the Etar app, and the Etar app upon being opened showed all of the calendar events that my Nextcloud instance hosts! Put in another way, the Etar app recognized the DAVx5-facilitated calendar data without me pointing the Etar app at DAVx5 or vice-versa.