how does airplane mode work on iPad?

If you are on an airplane, most carriers permit using Wifi and Bluetooth, even when airplane mode is turned on.

And in testing it in my office, I turned on Airplane mode on my iPhone, but my phone remained connected to Wifi and I was able open any website I wanted.

Perhaps this will help you --> Use Airplane Mode on your iPhone, iPad, iPod touch, and Apple Watch - Apple Support

Likely because you were connected to Wifi. It primarily cuts off cellular access, which can interfere with onboard airplane electronics.

I can't tell you how or why some settings sometimes change after an iOS update. But I'm glad you see you can browse the internet with Airplane mode enabled.