Main app's icons overlays in Nova Prime's widgets
what is its source: is it caused by recent change to Contacts or Nova Prime?


Rahul in comments has pointed the reason (thanks Rahul). It is an OS feature introduced from Oreo (and the likely reason you didn't see it earlier- service folks must have upgraded it while under repair). For more see Android Developers : shortcuts overview  


  is there any workaround or a way to get rid of this nasty little thing?


Long press on shortcut &rarr; edit &rarr; long press on photo &rarr;select theme  &rarr; Gallery apps &rarr; select photos and choose the contact photo, go back  &rarr; Done

A disadvantage is that you have a rectangular icon that won't match with other icon appearance . But that may be good too to differentiate contact shortcuts! 

I don't know how to fix that, unless you use a photo editor app that gives you round shapes (OP has suggested - you can use this Ukrainian on-line tool or this Russian on-line tool or search for some alternative).

And it is not for contacts only. I have a mail app which shows the same for "compose" shortcut. This app is targeted for min sdk 28 (Oreo). From August this year, all apps have to target Oreo and you will see this behavior uniformly

Tested on the latest version of Nova on Pie.