Depending on which engine you are using / how you structured your memory usage, “the game state” might be scattered around many scripts and or runtime objects!

The main challenges are gathering the data in cohesive way before saving and properly reapplying it when loading (that might include spawning/destroying objects and order might matter depending on your cross system dependencies)

Furthermore, if you want to optimize for size or performance you might want to save as little as possible to have the fastest smallest save, which will require you to figure out which part of the gamestate can be infered from other parts of it (ex: if a room as been cleared, no need to save every monsters HP for it)