The game mode allows you to play and test the game.
By default, all panels in game mode are hidden to ensure the focus on the gameplay. In the game mode, you cannot move and/or delete objects, nor edit animations.
For show left and right panels hit CMD + / for macOS or CTRL + / for Windows. Also you can go to Main Menu > View > uncheck Hide UI. Note, that some changes you make in the Inspector will be automatically saved when switching to a different mode. It work for Main Character Properties; Main Camera; Gravity.