From everything I can see, you did have to buy games on Stadia. They would give you a free game a month, but if that wasn't the game you wanted to play, you had to buy it. The base version of Stadia was free, but the Pro version gave you a discount on games - it did not make them free.
This is the official support forum and there are many Q&A's about purchasing games:
... If you have an Android device, you can also try via the Stadia app to purchase games (once purchased, you can play them everywhere, on mobile, TV or PC).