I love the strawberry maria, it’s one of my favorites!
The strawberry puree is the drained, uncooked fruit with the reduced juices added back to it, and then pureed. The sauce is just the puree that has been sweetened, nothing more. The additional sugar accounts for the larger yield of the sauce. But you’re not making the sauce, so skip that part.
The puree is meant to be a building block for other recipes, so it is unsweetened, allowing you to tailor the sweetness to whatever you’re going to add it to. You are making the cloud cream, so you follow the recipe, adding 7T of sugar plus one cup of the unsweetened puree (meaning fruit plus reduced juices). You can freeze the rest of the puree, it’s great sweetened and served over berries/cake, or over berries/ice cream, or saved for another cloud cream, or added to a buttercream.
I know it says “cooked” puree, and I’ve also wondered about that from time to time, but I’ve made this puree several times without cooking the finished puree and it’s fabulous, very fresh tasting (the juices get cooked, of course, but not the fruit).
Good Luck, and enjoy!