if I upgrade a game for xbox series s, and play the upgraded version on my xbox 1 will it...

All Xbox One games can be played on the Series S/X via backwards compatibility. Kind of like how you can play 360 games on the One now. You would be playing the One version of the games.

With Cross Gen Editions/Smart Delivery, you're buying the One version and get an upgrade to the Series S/X version of the game when you get the new console instead of having to buy the Series S/X version and you an take advantage of some of the upgraded
features.

Hi! I'm Rostom, an Independent Advisor. I will be glad to help you here.

I believe that you installed the game as Xbox One version. That's why it's giving you that label. Check this link https://www.xbox.com/en-US/games/store/the-call...

If you want to upgrade to Xbox Series X/S version of the game, get the upgrade here https://www.xbox.com/en-US/games/store/the-call...
After purchasing the upgrade, search in the Xbox store for The Callisto Protocol:tm: for Xbox Series X|S to install the Xbox Series X|S version of the game.

Yes. If you buy the cross-gen bundle, you'll get the Xbox One version and the Series S/X version. Even without the next-gen upgrade, you'll be able to play the game via backwards compatibility.

I’m trying to run the Xbox one version on a Xbox series s. Could that be the issue? Do I need the cross gen upgrade?

NO! Unlike some games that have an Xbox One version that will upgrade to the the S|X version if you put it in a series X, NBA2K for S|X is a complete different version than the Xbox One version and it will not work if you put the disc inside of an Xbox One. Xbox One cannon run a Series X game and putting a Series X disc inside an X1 will not install the X1 version.