wikipedia has a list:

https://en.wikipedia.org/wiki/Parental_leave#By_continent

it also lists pay, which seems to be a range of fully paid for part of the time, then partially paid and finally unpaid.

so in many cases you can only get the full 3 years if you can afford it, but having your job protected, knowing that you can go back to it is still better than outright quitting.

Based on what I’ve seen, there is no state sponsored parental leave program anywhere that is compensated at full salary, except perhaps for very low salaries.

I'm unsure what you've seen. Most countries in the world compensate at full salary: https://en.wikipedia.org/wiki/Parental_leave#By_continent

it is usually only for the first part, but not for the whole time, unless the whole time is short. i haven't seen any that pay full salary for more than a year. and 3 years pretty much always had some time unpaid.