From the Xbox Series X without space to install more games, to the Xbox Series X without...

So I can't even play the game on my Xbox series X controller without the guitar also I can't play the disc version on my Xbox series X

From what I can tell, to access the Series X version of the game, you need the Cross-Gen bundle...once you buy that, you should then be able to download and install the Series X version. Without the cross-gen bundle it will, presumably, just install the XB1 version

From the Store page:

"For digital owners of the Call of Duty®: Black Ops Cold War Standard Edition, this upgrade will unlock the Call of Duty®: Black Ops Cold War Cross-Gen Bundle, giving access to the Xbox Series X|S version of the game. After upgrade purchase, search in the Xbox store for the Call of Duty®: Black Ops Cold War - Cross-Gen Bundle to install the Xbox Series X|S version of the game."

Hi there.

Thank you for reaching out to the forum. Unfortunately not. All Series S/X and Xbox One Games with Smart Delivery, thoughs have to run from the internal storage or expansion slot drive. But for Original Xbox, X360 and
Xone game without enhancement, they should still run fine from your external unit.

More information here:

• A Primer on the Simple and Custom Storage Options Available for Xbox
  Series X and Xbox Series S at Launch.

I don't know if these server problems are related to the updates they do for the game.

I remember not long after I installed the game on my Xbox series x last year it received an update a day or 2 later and I started getting a server error message on my Xbox series x yet on my Xbox one x the game played fine without an error message.

Hi,

Your drive will work the same on Series X as it does on Xbox One and you won't need to format it.

However, Series X games or Xbox One games with Series X enhancements will not run from that drive and will either need to be installed internally or to an external SSD designed for Series X/S.

Your hard drive will be too slow for Series X games. They can be stored there, but not run from there.