Web Socket Secure URL Encryption

Is the URL itself encrypted as well when using wss://? For example, say you have a simple Sinatra web application that accepts web socket connections:

class App < Sinatra::Base

  get "/ws/:api_key/room/:id" do |api_key, id|
    user = User.find_by(api_key: api_key)
    room = Room.find(id)

    if RoomAuthenticator.new(room).authorized?(user)
      request.websocket do |ws|
        ws.onopen { publish(room, "#{user.name} connected.") }
      end
    else
      401
    end
  end
end

Then from the client/browser, in JavaScript:

new WebSocket("wss://" + window.location.host + "/ws/" + user.api_key + "/room/" + room.id);

Is the user.api_key in the URL encrypted or is it susceptible to attacks?