Is there a successor project to Omega 4?
I found what looks like an explanation from 2016. It looks like Omega 4 is not going anywhere.


  ...both new Omega versions (7.x-5.x, 8.x-5.x) probably have nothing in common with (7.x-4.x) and are not the successor of Omega 4.
  
  The successor to (7.x-4.x) is new project Khan so all the questions about that should be posted there. Truth to be told, there is not much activity there, since.
  
  So if you wish to make some sort of continuation of current 4.4 code base to D8, probably you will have to do it yourself. Personally, I do not think it will make much sense as the differences between D7 and D8 would not leave much in common.


The same user asked what the status of Khan is two months ago and hasn't received any reply. In another thread, the maintainer posted that Khan is postponed indefinitely:


  ...This is a serious project but since I am currently focusing on GraphQL for Drupal you can consider it postponed until I am done with the first release of that module.


So it seem fair to conclude that there is no Drupal 8 successor to Omega 4 at time of writing. 



Life is too short for drama, so I personally am going to (reluctantly) drop Omega and switch over to Bootstrap.