GameMode is not persistent across levels. This means that anything you set in GameMode for specific level will be gone when changing levels, even if the two levels uses the same GameMode class.
To save your menu data into a persistent class I’d suggest using GameInstance. GameInstance is persistent from the second the game launches to the second it ends.
You can use the levels blueprint to set the values in your GameMode when the level loads.
You want different game modes for different maps. I highly recommend having a GameMode specifically for your menu map, and a GameMode specifically for your game maps.
So, save your data to your GameInstance when pressing play, and load them from GameInstance into your GameMode when the level loads.