So here's something interesting, as this happened to me...
I live in Taipei.
This just recently started giving me issues. When I set my internet up with a new company (changed it from a shitty one), they gave me a modem that was really pathetic in terms of build quality and performance. When the guy came to set up my network, I had him create a bridge between the modem and my $150 ASUS dual-band router. Naturally I set my PS4 network up to that with a wired connection.
I got my Pro, everything was fine, until a couple days later I started getting the WS-37397-9 error.
Even when I try to access the PlayStation Store website from my Macbook on a wifi channel from the ASUS router, it errors out. I can't get into Sony related services using the ASUS.
However, when I plugged my PS4 Pro directly into the shitty modem (there's a bridge between the modem and ASUS), I stopped getting an error and everything connected fine. Furthermore, when I access a wifi channel from the modem with my laptop, I can access the PSN store again.
So, WTF?
Hopefully this will rectify itself as it did for OP.