There has been a lot conjecture on how the Stadia Pro’s “free”games would work. The messaging has been mixed by both Stadia themselves, media and gamers. The work library seems to have been causing the confusion. Stadia have now confirmed that it will follow the Playstation plus model.
This means one game, possibly more, is given to Stadia Pro users. These “free” games are then built into a library of games for the user. This looks where the confusing language has come from. With that you can only access the games while you are subscribed to Stadia Pro.