Hey. I added a "Load Game" button to the Title Menu where you can load a game, like usually the "Continue" Button does.
Now I want to program the actual "Continue" button in a way that it loads the most recent save or quicksave.

So basically I need to get all quick saves and all saves and check which one is the newst. Does anyone know a viable approach to this?
I currently even fail to load all Save Files into a C# Variable at all :/

You can override SaveLoadMenu and use the Slots variable of the GameStateSlotsGrid to pick the most recent save state. Each GameSateSlot has a GameStateMap which stores the SaveDateTime.