If I play CoD Coldwar on playstation and later get it on xbox series x, are the data still saved?

I currently have a Playstation 4 and would like to wait until the xbox series x comes to a normal price or until it is available, it will take a while.

However, I want to get CoD Cold War NOW. And since, as far as I know, there are now "activision accounts", data would have to be saved. Or?

Short:

Does Call of Duty store data independently?

Online you should be able to use your Acc as normal. However, you actually lose access to one of the special zombie modes.

However, the campaign save will be gone.

Yes, I mean the weapon camouflages etc.

I don't care about the campaign

And what do you mean by access to a special zombie mode?

There's a zombie mode that is exclusive to PS for the first year. It is not accessible via Xbox. The weapon camouflages are linked to your account. If you want to be on the safe side, you can simply ask Activision Support. I have the same account with Warzone as on the PC & have the same weapons, camouflages, etc. On the Xbox.

Thank you very much 🙌