Yes that is normal. Season passes are not platform licensed, but are rather in-game unlocks/purchases. They get assigned to the platform's characters that first log in. While you may have been logging in on Steam you were logging in with your Stadia characters as the active characters which means your season pass was assigned to your Stadia characters. If you go log in on Stadia you will find you still have access to the season pass on those characters. If you wish to have access to the current season on your Steam characters you will need to purchase a season pass in-game from Eververse.