Thanks for your reply.
Here is a link which describes the process for the Asset Store: https://support.unity3d.com/hc/en-us/articles/208468576-How-do-I-create-upgrades-for-my-assets-
It might be not as relevant for games, but for apps/applications it would be quite a good feature on itch.io to have.
I am considering going a different way for my specific project now. But there I also have a question before I can do that. My plan is to upload a new a file to the same project and change the price to be more expensive, so that I have two differently priced files in this project. Will the users buying over the "Widget" be able to choose which file they want to buy, or do they have to type in the amount by themselves to unlock the more expensive file? It would be no problem if they get access to both files if they pay for more expensive file. But it should be as easy as possible, because most of my payments are done via the Popup/Widget.