Do I see it correctly that this tracks progress globally?
So if I have 2 games running with one of quest. And i finish one game. Does it update in game additionally to the progress I have achieved in the still active quest?
So e.g. 1M gold quest i have 2 games running with that quest. One has 200K and the other has 300k. I finish the first does the quest in the second show 500k?
Also I expect that deleting a quest will remove it from the ingame screen?
No the quests will work the same as before.
When you start a game, the quests of that game are exactly those you currently have and they stay the entire game, no matter what happens in the main menu.
Then, once you submit the game the quests are processed and booked if you currently still have those quests active.
It is just a visualisation to see what quests are active in a specific game.