I actually clean flashed, rooted with Magisk (I usually use supersu), and tried with all three variants of Adaway in the OP. In each case, Adaway worked perfectly, but if I denied su access (Magisk manager -> three bar menu -> supersu -> turn off switch for Adaway) then I'd get similar results to your log.
I don't think this is an Adaway problem.
Maybe you could remove supersu permission for Adaway then restart Adaway. At least Magisk should respond with a prompt to grant access. If it doesn't, then I don't know what to tell you. Maybe you'll get better help in the Magisk thread. I'm on a Nexus 6 so the difference to an LG may be at issue.