After unsuccessfully changing the branch from 'latest' to 'dev' and running chmod -R 777 /mnt/user/appdata/pihole/ I found a solution:
In my docker config I changed /mnt/cache/appdata/pihole/pihole/ to /mnt/user/appdata/pihole/pihole/ and /mnt/cache/appdata/pihole/dnsmasq.d/ to /mnt/user/appdata/pihole/dnsmasq.d/
All the error message seem to have gone away.