Google Analytics Goals/Conventions for successful payment page

I have a member registration process with a few steps and then going to the membership plans. select the plan and then pay. so it is going to the shopping cart page. then they will pay.

This is my problem. Registered Users are coming to the shopping cart page. (ex: website.com/cart) But even after completing the payment, the page URLs are the same. (still, it is website.com/cart) But it is showing the Invoice details with orderID and everything on the screen. But it is not changing the URL.
I want to set a goal who completed paying the membership payment. If we set the shopping cart page URL as the final URL but users will leave before making the payment also. I just want to get only the successful payments through this Goal. Please, can you advise me on the things that we can do? I really appreciate it if you can support me.

The website developers are from another team and they do not do anything major changes since it is in a shared environment. So they will not do any changes to the website since it is affecting their other clients. I just requested to point to a ‘thankyou’ page. But they are not ready to do it. So what we can do about this?

How can I use Google Analytics and Google Tag Manager for this?

Please, help with your knowledge. Thank you very much!