Just in case a dev will have a look at one day in future:

I tried a "stress-test" with my gaming laptop ( Acer Predator G9-792, Intel(R) Core(TM) i7-6700HQ CPU @ 2.60GHz, Windows 10 64 Bit, Intel(R) HD Graphics 530,  NVIDIA GeForce GTX 970M, 16GB RAM), for to check out, if I get the same experience as others users reported (I usually play on my other rig). Did set game settings to max. number of players (12) and largest galaxy seize. I expect the bug to be reproducable.

This save file is the one, when endless pending turn started. I did save and reload and was able to continue to next turn.

Ungefallene turn bug.sav

This save file is of next turn, endless pending turn bug did reappear and I wasn't able to save.

AutoSave 11147.sav

Diagnostic file (even zipped one) rejects to upload at the moment.