Hi @Ice.Dragon 
welcome to the community!
Instead of relying on URL parameters (which can sometimes break the order summary/order bump modules), I’d recommend using sessionStorage to pass the selected product/variant across pages.
That way, you don’t need to modify the checkout URL at all — and your modules will continue to load properly.
Here’s a detailed example you can follow: 
Selecting products on funnel landing pages
This approach stores the chosen product in sessionStorage on the sales page and retrieves it on the checkout page, ensuring smoother functionality.
Give that a try, and let us know how it goes! 