I don't know what base44 is, but from what you're describing, neither Itch nor Steam will help you.
Itch and Steam are game stores where the user buys a game. When they buy a game, they have unlimited access to that game's files (they can download and play it as many times as they want).
What you need to implement is a Usage-Based Pricing system, and no well-known digital game store will offer that, because it's simply not the way digital games are sold. You could even violate those stores' TOS, since the buyer is expected to be able to use the game as many times as they want.
You also can't sell unique keys from these sites; Steam doesn't allow it, and while you can sell many types of files on Itch, there's no tool that allows you to deliver a unique file to each buyer. (EDIT: One correction, in Itch you can associate unique external keys, but you have no way to separate them by price/number of uses and it is only one key per account.)
To implement a Usage-Based Pricing system, you must do it entirely on your own on the server side. You need the key you sell to function as a user account with an associated counter. In the digital version of your game, upon startup, it should request the key and authenticate against your server, where you deduct a usage and send the application a signal indicating whether the key still has usage or if it's all been used.
How do you implement this? It's something that has nothing to do with Itch, but I think the term you should look for is "Licensing Controls."
If I were to develop what you have in mind, I would start by Googling something like:
"How do I implement a Licensing Controls with a counter?"