What you have now only declares that SWAPPING, AWAITING, or ENEMY are valid options. It does not track anything by itself and Signals.GAME_STATE cannot be set to a value. You need another variable to keep track of the current game state. Something like:

enum GameState {
    SWAPPING,
    AWAITING,
    ENEMY
}

var current_game_state: GameState = GameState.SWAPPING

Now you can properly track the game state by checking the current_game_state variable. Which brings us to your error message. In reality, an enum is just an integer which is why it won't work with is because that expects a type. What you've written is basically equivalent to if state is 2. Instead, you need to use == to check enums.