Yes, the border was closed to all foreigners at the very beginning. You can now come even as a tourist if you want, but it's a mandatory two week quarantine at a designated hotel with two tests.

You don't have to show any papers to enter any store but you do have to temp check.

Contract tracing when someone turns up sick, but there hasn't been a single case of that here in almost two months

Yes, they feel patriotic about it here and everyone wants to do their part when they see how poorly other countries have done, the depressed economies, joblessness, lockdowns, joblessness and sick people. They don't want their country to become a shithole like that.