I wasn't sure how it would work, but when you start it there is a popup:
I have to get the other volumes installed through the app. I had installed them before having the app. (I don't think it even existed back then.) Anyhow, inside the install folder there is another folder named .itch with a receipt.json in it. It's the only extra thing included when downloading via the itch app, so I'd guess that's where the launcher info is.