Share PoE2 from Xbox to Steam

Hi here, I've bought PoE2 within MS store (Xbox), linked the account on this website with Xbox account and Steam account. I expect to be able to play the PoE2 on Xbox and Steam now (even w/o synced savings), however I don't see PoE2 within Steam acc, how can I add the game there? More over, this website says me that I don't have PoE2 game, but I can see 300 gold on my wallet (starting pack for PoE2)