Also been having this issue, but I have usually been able to save and reload because it was just a buggy anomalie that my surveyor ship was exploring and it got stuck on it and was unable to finish moving.
This time however, at turn ~645 all my survey ships, colony ships, scouts and constructors finished moving, the drengin race finishes moving and then sometime after A.I Sentinels (my custom race I created) finished moving and before the Yor collective start their turn, the game gets stuck in limbo. I am at war with the A.I sentinels and am at peace with all other races, and normally they attack my star bases or undefended ships but not that turn for some reason. There is a constructor within range of one of their fleets and their fleet doesn't move or try to attack which is odd. So I believe that is the case, something in the battle sequence has become bugged.
Another thing I've noticed is that the Ultra Terriforming research tech name & improvements got changed to "OmegaTerraforming_Name" all across the board
Perhapse if there was a save file editor I could edit their disposition towards me and view all of their ships in order to find where the bug is coming from.