No such requirement here in Europe and Scandinavia as far I know. And while it is overwhelmingly likely true that domestic cats are significant predators in Australia where they were introduced only recently it's not quite so certain that they have the same effect in Europe where mammalian predators and their prey have coexisted for millions of years.
In Norway in particular where the average human population density, and hence domestic cat density, is low and the countryside forested and fertile the impact is probably fairly small.
I found this on the Smithsonian site:
Australia’s Cats Kill Two Billion Animals Annually.
Here’s How the Government Is Responding to the Crisis
A new report from the federal parliament recommends cat registration, nighttime curfews and spaying and neutering
..
Cats arrived in Australia with the first European settlers in 1788. Within 70 years, cats had spread throughout the country; cats now inhabit 99.9 percent of Australia’s total land area. On a yearly average, an estimated 2.8 million feral cats roam the continent, but according to John Woinarski, a conservation biologist at Charles Darwin University and co-author of the book Cats in Australia: Companion & Killer, this number can balloon to 5.6 million in years of heavy rainfall.
https://www.smithsonianmag.com/science-nature/australias-cats-kill-two-billion-animals-annually-180977235/
How robust those estimates are I have no idea but it suggests that anyone hoping that registration and a curfew will have an immediate effect is going to be severely disappointed. It will take decades, if it works at all.
