Got exactly the same problem here on an iPad Air 5th Gen running ipadOS 16.1.
The handwritten notes are no longer visible in iCloud Web.
They just show up like in the screenshot posted earlier by Daniel-Mi.
Also there seem to be some other problems I encountered with the new ipadOS 16 notes app:
- After taking handwritten notes for longer periods of time (e.g. >45 minutes) the writing starts lagging behind the pen movement and eventually sometimes the screen flickers purple. When erasing some handwriting and redrawing over the same area, the erased strokes flicker through. This is accompanied by the iPad battery draining pretty quickly (-30% in 1 hour) and the device getting unusually warm.
- The issue in 1. seems 'fixable' by restarting the app. Only problem being is that sometimes doing that, the last taken notes just disappear and are lost.
- I've already tried reinstalling the notes app and restarting the iPad. Got me to nowhere new.
I hope they fix this by a future update.