It seems that I have managed to really turn of the Wi-Fi now.
Possibly I have did something wrong but after some resets and closing of all the Wi-Fi options again now the Wi-Fi is off also in the battery stats.
This also seems to help with the battery since now the battery drop is less. After charging it fully and leaving it standby all night (8 hours) it has dropped 3%, with data on and wats app but with 0 screen on time . This is more what I was expecting and today it seems to be a bit better. However the battery does skip some % (drop from 97 - 94) every now and then but this will probably be better in time. (I have already did a full cycle of fully charging fully discharging and charging when the phone was off with low power charger).
So for me a conclusion so far is:
If Wi-Fi is on in your battery stats it is on and it can be turned off.
Google Location tracker that tracks your every move all day is a very dumb default setting and turning it off helps.
With this I think battery life is acceptable.
I will update after some days to share my experience.
Edit: what still surprises me is that Google services is still the biggest battery drain (sorry i can post pics links because I am junior member i can post links). This even when I have used internet radio for 1 hour and Flitsmeister (an app that tracks my GPS and warns me for speed traps on the highway), my screen was off during this hour.