Is there a way to update my iPhone 11 if I suspect Apple's servers are down causing the error?

Yes, if you suspect Apple's servers are down, you can try again later, as server outages are often temporary. Alternatively, try updating your iPhone 11 using iTunes or Finder (on macOS Catalina or later) on a computer. Connect your iPhone to the computer with a USB cable, open iTunes or Finder, select your iPhone, and check for updates. This bypasses the iPhone's direct connection to Apple's servers during the initial check.