This morning I loaded the Minecraft Launcher and it prompted me that is now possible to add Microsoft Accounts. So I did it, but now I got two accounts in the Launcher. The first is my Mojang account with which I can play just fine. The second one is an account created after adding the Microsoft Account and it says that I don't have the full game (which of course is not true since I already got the Java Edition of the game with a Mojang Account). Plus, if I login with the Mojang Account, I didn't have any cape as promised, so I think that the account linking is effectively not working...