To preface, I know there is an option to download a game, but this question is more for web-based games. I am also aware that users can go through a process on their devices to add shortcuts through their own settings or whatever method is required, but the thought was to remove that entire process for the convenience factor.

So I was wondering there is such a feature - whether through the game description or during the game's setup process - where users can add that project's page as a shortcut to their desktop or home screen if they're using a mobile device.

I didn't quite understand the question. As I understand it, you're talking about creating shortcuts on your desktop that lead to a specific website. If so, it's as simple as using the built-in share feature. However, this requires manual intervention, and it's not possible to do it programmatically if you're using itch.io instead of your own hosting service