I figured out why the game gets stuck.
The reason is that when you switch a current player from Human to AI the flag IS_CURRENT_TURN (civ6-save-parser/index.js at master · pydt/civ6-save-parser · GitHub) remains set true.
It does not interfere with turns when this flag is set true for AI but when you switch back this player from AI to Human you end up with two players with this flag set true.
A solution to that would be force resetting the flag to false in the save file, then the game becomes unstuck.