From your link:https://en.wikipedia.org/wiki/List_of_Star_Trek:_The_Original_Series_episodes <-- they're a bit erratic but I do see a pattern. It suggests they're running parallel to TOS now.
So the stardates on the Discovery could be different than on the Enterprise and other ships.The progression of stardates in your script should remain constant but don't worry about whether or not there is a progression from other scripts. Stardates are a mathematical formula which varies depending on location in the galaxy, velocity of travel, and other factors, can vary widely from episode to episode.