Platformer game level rotation

Hi all, currently I am building a platformer game that uses first person control and camera . There will be a minimap that shows the whole game level in 2D or orthographic view.

So, my question is that I wanted to implement a mechanic like the game "The Adventures of Shuggy" where the player can rotate the game level 90 degree. How can I do this?

I had tried using the "eulerAngle" to rotate the FPS character but the result is weird and the gravity not function which the character should fall to the bottom after the rotation. Is the rotation suppose to be applied on character and camera or the platform? The rotation will only need to be 90 degree and along Z-axis I guess.

Sorry for the long question still new to unity. Thanks for your help