Sorry.
But … I got encouraging results with Easer (since the highly praised Tasker is a paid App in the Play Store) …
- (Gave Easer every possible permission by starting the App several times until it didn’t complain anymore)
- Outline - three-dot-menu - Stop
(I don’t know whether it was in the “Running” state per default or whether I tapped on something by accident at first, but I didn’t want it running while fiddling around) - added a “Condition” - Screen Status - On
- added a “Condition” - Screen Status - Off
- added a “Profile” - WiFi - (setting enabled) - toggled On
- added a “Profile” - WiFi - (setting enabled) - toggled Off
- added a “Script” - Profile - (profile with WiFi on) - Use Condition - (condition with screen on)
- added a “Script” - Profile - (profile with WiFi off) - Use Condition - (condition with screen off)
- Outline - three-dot-menu - Start
Well, while to me Easer seems not very intuitive, this seems to do the job for me for now … I can see WiFi is off at the moment when I turn on the screen, and then WiFi is reconnecting immediately 
.
I’m open for more efficient Easer proceedings for this.
And I hope running Easer and using the mobile network for the background tasks I still want to run don’t eat more battery than WiFi 
.
Edit: I tried to replace the Conditions with Inline Events in the respective Profiles (which would have rendered the steps to add Conditions unnecessary), but with no success … so this FAQ seems somewhat credible when it says you should use Conditions instead of Events.