Buy COD MW again for the PC if I already have it on the Xbox?

I bought Call of Duty: Modern Warfare as a disc for the Xbox. That means I have unlocked the multiplayer mode, the campaign and the co-op mode and can also play them. I finished the campaign in 2 days and the multiplayer works perfectly.

The only problem is only when I download the Battle.net Launcher on my PC, log in (With the same Activision account as on the Xbox. (On the Activision website I linked my Xbox account with my Activision account.)) And then Install Warzone, start the game and try to play multiplayer, it doesn't work, but I have all the weapons and levels as on the Xbox.

So do I have to buy the game again for 70 euro?

Yup lol

So do I have to buy it again? D

Ja

Since Call of Duty: Modern Warfare (2019) does not support Xbox Playanywhere, you have to buy it separately for each platform. But you won't end up at 70 euro, because as a key it costs almost 53 euro with us - https://www.keyfuchs.de/game/call-of-duty-modern-warfare-2019-key.