One possibility is that the VPN server IP is detected/blocked by PBS or by the auth partner they’re using so can try swapping server/rebooting Roku
I’m assuming you’re connecting to United States Surf Shark?
OpenVPN isn’t likely to make a huge difference tbh
If you’re open to a temporary workaround to generate the code (this works on some apps):
- Connect your streaming device directly to non-VPN internet - actually do it on non-PiFi so just regular wifi.
- Open PBS app, get the sign-in code.
- Go to PBS App Sign In and enter the code.
- Re-enable VPN router after successful sign-in.
P.s If code shows on regular wifi but not PiFi with VPN off, then it could be AdGuard Home related. See how to disable that here How to enable/disable adguard on Pifi - #2 by pifi