Cold was gone?

I linked my Activision account on the PS4 to my Blizzard account on the PC, on which I had already bought CoD Cold War. When the link was complete, I wanted to play Cold War on the PC. Strangely, however, Blizzard is now showing me that I don't own Cold War and that I have to buy it.

Does any of you have any idea how I can get Cold War again?

I'm also switched from the Ps4 to the Pc. The account can be transferred, but unfortunately you have to buy the game again for PC, it will not be transferred.
Unfortunately it is like that.