I dare say all online stores keep a record of your purchases. It's just a question how you can browse those purchases. The wallet on Steam is like a, well, a wallet. It lists transactions, which often are purchases, but can be other things, like refunds, increasing funds and such.
Itch has no list, but I guess it is because they have no wallet and everything you can buy is either a project or a bundle. So they just list all bundles and projects you "own" in your library in their library view. Hmm. For a collection there is two ways of displaying it. I wonder why there is no list overview for the purchase library. Or a hide function for the people that make that purchase list public, but do not want to show all things they bought. Itch does lack a lot of features one might expect.
