Do i need to re-buy cod cold war to play on next gen?

Looks like you can upgrade to the cross-gen bundle:

https://www.microsoft.com/en-gb/p/call-of-duty-black-ops-cold-war-cross-gen-bundle-upgrade/9mxpqc207hnm?SilentAuth=1&wa=wsignin1.0&activetab=pivotverviewtab

Once you have this you'll need to go to the Mircosoft Store on your Xbox and re-download the Series X|S version.

I currently have the Xbox One S and the standard edition of Cold War installed. In a few weeks I’m going to get the Xbox Series S and I was wondering if I have to buy the Next gen version for Cold War at it’s full price.

Thank you

No you don't just buy the cross gen bundle for 10$

I crash on 2k21 next gen version. Some on cold war. Sometimes even on the dashboard.

The XboxOne version doesn't get the HD assets or the ray tracing. To get it you'll need the next gen game, ray tracing will only be available to you if you have a TV that supports the 120 fps. But the HD assets should be added back now that Activision had fix the issue it was causing, but dont worry about it, because there is no difference. You'd just be wasting 50GB of space. If you want the Next Gen of cold war all you have to do is go on the Microsoft store and buy the next gen upgrade for 10$.. unfortunately it isn't free.

I just reset my xbox and reinstalled CoD Cold War and it’s still asking me to buy the game i had preorderd the ultimate edition when the game was on preorder and have played since day 1 of Cold War and this has never happend till yesterday