I’ve used DAVdroid for a while in combination with my own Nextcloud server. Works perfectly fine: I have an overview of my own and shared calendars on my phone and sync as expected.
I just changed in Nextcloud the permissions of a shared calendar, so that I can now also edit that shared calendar. It works in the Nextcloud web-interface. However, when I sync in DAVdroid, or Etar (my calendar app), then the permissions don’t get updated. In other words, in DAVdroid I still get the icon.
Instead I suspected that I now should get write access to that calendar (I guess removing & again installing the account works, but just wanted to check first).
DAVdroid debug info