No sound while playing Apple Arcade games on Mac

When I play a game downloaded from Apple Arcade there is no sound. For example, I downloaded Castelevania, the app loads, the Apple Arcade splash screen plays (no sound), and the game start screen loads (still no sound). When I start the game everything seems to be fine with the game, but there is still no sound at all. I deleted the game and reinstalled it from Apple Arcade and it still did not play any sounds. I deleted the game again and tried another game, Fantasian, and it was the same situation. This time the Apple Arcade splash screen played its chime, but once the game started there was no sound at all. Also during the Apple Arcade splash screen a little notification appears in the top right saying that "game mode" is turned-on.

By play sound, I am simply trying to get the game's sound to come through my Mac Studio's built-in speaker. I do have external speakers, but they are not plugged in at the moment. In Settings, the Sound setting shows that sound output is set to "Mac Studio Speakers" type "Built-in". All other sounds from macOS and all other apps play sounds correctly. I can have Apple Music playing music correctly through the built-in speaker, then launch the Apple Arcade game and there is no sound coming from the built-in Mac Studio speaker. Also, no Focus modes are set for this mac.

After reading some of the other community questions regarding no sound in games, I tried bluetooth headphones connected to my Mac Studio before I launched a game, and once the game started the game's sound was playing correctly through the bluetooth headset. There apparently seems to be a setting somewhere that has Apple Arcade games use bluetooth only for sound, and I would like to know how to turn this off so that I can have the game's sound play through what I would like to use.

As far as I can tell there are no settings or preferences anywhere for Apple Arcade or game mode in macOS. If the game is in full-screen mode, then game mode automatically starts up. Even when I take the game out of full-screen mode, and also turn off game mode from the status bar icon, there is still no sound in the game. Any ideas?

I am on macOS Sonoma 14.5, using a Mac Studio with a M1 Max chip.