It is not the 1st time I have this issue, and it happened also, from time to time, in v 4.0 and cannot recall this issue in other versions.
Currently a GC3 Steam play time of 1344.8 hours, and 80% of my very few issues have been during the end turn phase.
In this case, after 50 hours in a new 4.1 game, turn 162, the game is stuck when processing the move of the last (customized) faction - The Angelic Host - I have for 6 years now, with 0 trouble with it up till now.
The image below shows that the "WAIT" button is still showing, and greyed. Print-screen taken 3.5 hours after it started (and coming back from a loooooong walk with my 2 happy dogs - they say thank you to the bug !!).
Access to the game is fluid, as if all processes are done, and it is just stuck at the point. The resource monitor shows a constant and regular use of CPU and GPU, all quiet.
I have seen ships from this faction moving, and then all got . Not frozen, I can browse all menus/windows, scroll as if it was my turn, it is just inactive.
The game is on a custom map with added planets for fitting the numerous factions, immense, 68 starting civs (but a lot lot less now), all customs and existing/played continuously since 2016 (krbjms in Nexus/workshop), godlike difficulty, slow research, slow pace (which is not : this does not work with large and long games...)
The saved game is huge : 145Mb, 7zipped 127 mb. The uptobox link is :
https://uptobox.com/pg2o58giwnxd
I just hope this can be fixed/stabilised, as, if a day I can find a AMD 6900XT GPU ... (sigh), and with a 16 core, 64 Gb Ram, I do intend to play the ludicrous map with 100+ civs ! I will jump in the river if, after +100 hours in a game, I am stuck in a end-turn ...