QNAP docker pi-hole has been pretty hit or miss, I haven't seen much of a fix other than reinstalling container station.
I am wondering why it does not have any permissions since I changed them so it should have it.
Did you still have errors after chmod 777 on setupvars
The stock permission is enough typically, other's read -rw-r--r-- works fine in my tests on stock docker.
Related thread : PHP permissions error web admin page
Stock docker is all I have to work with unfortunately so if there are any code fixes that are needed I’ll need some direction from community members custom hacking the image (or maybe container station) to see what fixes things.