It’s been a while since I’ve worked with universal linking, but doesn’t Apple’s APIs allow you to carry context? Or at least preserve the URL so you can take the user to where they were? I don’t think you need to hijack the pasteboard just to continue the users flow.
You definitely do for the first launch post install.
The flow is click link, copy data or finger print, redirect to the App Store, install, user opens app for the first time, route to experience from finger print.