How do I actually check which keys are being used?

I'm pretty sure you used the wrong service. ContextActionService binds a set of inputs to a function. To bind a function to a keyboard button with this service, call the function BindAction. So, to print a string when the W key is pressed, a function can be bound like so:

function onKeyPress(actionName, userInputState, inputObject)
	if userInputState == Enum.UserInputState.Begin then
		print("Forward")
	end
end
 
game.ContextActionService:BindAction("keyPress", onKeyPress, false, Enum.KeyCode.W)

UserInputService binds functions to input via its events, such as InputBegan or InputEnded. These events fire on any input change, so it is important to check for the particular input you are interested in when handling the function. So, to print a string when the W key is pressed, a function can be bound like so:

function onKeyPress(inputObject, gameProcessedEvent)
	if inputObject.KeyCode == Enum.KeyCode.W then
		print("Forward")
	end
end
 
game:GetService("UserInputService").InputBegan:connect(onKeyPress)

I think you needed to use UserInputService instead of ContextActionService. Try that. If it helped, upvote and accept answer. Thanks! (Snippets of code are from the wiki, same with the description on ContextActionService and UserInputService)