You’ll only have access to previously claimed games if you have an active pro subscription. In the case of Destiny 2 the base game is free to play on Stadia, so you won’t need Pro to access that...however, I believe that you will only have access to the expansions if you buy them or you restart your Pro sub.
Note that Beyond Light is not included for Pro, so you would need to buy that one if you wanted to access the new storyline / content.
