Not sure why but I'll post an update to note that I am now experiencing turns/saves at a tolerable pace again.

The game has memory leaks that are unresolved. Also, if you have tons of saved games that slows it down too

Try clearing the Saves out and reset

Two things come to mind:

1) (unlikely) maybe the saves take up too much of your hard disk space. Each save is quite big (3 MB or something) and they are generated in an endless fashion. So eventually you might run out of space with autosaves turned on.
At least there is a button to clear all saves except the last 50 or so. It only pops up when you are playing, not in the main menu. Maybe try that out if you haven't already.

2) I haven't played the game in a while but I remember turns randomly taking much longer than usual for periods of time. It always returned to normal eventually though. But if the game starts with long turns already I'd probably rather be on the safe side and roll a new map...

I have also found that sometimes assets glitch and cause delay/ crashes. Sometimes if you ignore that asset or approach a different way you can work around it. Sometimes a new map is what Has to be done

Holy smokes those turn transitions though.

I deleted the saves and it did not help. I was playing without trouble yesterday (though the turns were still slightly long), but today I just can't play. They are too long.