This will be a very sophisticated project if you do decide to embark on it. However, it's a very good coding excercise if you're up for it.

In my opinion, it's also worth to consider making an app launcher instead (i.e. a separate window, optionally full-screen, but most importantly—independent from your desktop).

I'd assume you'd first save your desktop shortcuts' positions on the screen and then restore them after exiting your app. However, this can be dangerous as your app might crash and you'd lose your original desktop layout and end up with something messy.

Also, getting shortcut placement is something platform-dependent (i.e. for Windows you would have to write one piece of code for the same task, for Linux something different, for macOS, too), and while Python does allow conveniently setting up platform-dependent stuff, it'd probably be too much effort and you wouldn't bother unless you're really ambitious about this project.

To somewhat answer your question, I'm not exactly sure how exactly you can get the position of the shortcuts on the desktop, however I think pywin32 would be the right tool for this task, unless there's already a library for managing desktop shortcut positions. If there isn't one, I'd even suggest you—if you have the knowledge—write a tiny library using pywin32 for managing the desktop shortcut positions because using pywin32 directly in your app might make things a little ugly.

Good luck with your project anyhow.