[2023] Authentication error after purchasing R6S on steam

I previously purchased Rainbow 6 Siege on steam and am trying to login to my 8 year old ubisoft account that i did not own R6S on. When i launch Rainbow through steam and login in to my old ubisoft account, which again, does not own rainbow, i get an authentication error saying the account doesnt own it but i had purchased it through steam. Did i open rainbow on the wrong account upon first time set up?