Surely this breaks the "email is not on same device as login" use case? At least with normal magic links, they're merely incredibly annoying but doable (via e.g. typing in the URL)

That use case still works. In fact it works better because if you click the link on your phone you don't automatically get logged in on your phone browser (or your email client's in-app browser). You can then copy the same link on your desktop and it will work as expected.

I'm confused. How do you get the cookie from the original device to the other device?

It's the other way around. You copy the URL to the device that has the cookie.

How do you copy the link between devices? QR code?

As long as you also have a code to enter, then things will feel fine across devices.

After reading the other replies, this seems like one of the more effective approaches. Thanks!