You have discovered what many of us have discovered. Astonishingly, the new Google Nest cameras that all of us purchased in the fall of 2021 do NOT work with the Google Nest app and do NOT show up on the home.nest.com website where all of our other Google Nest cameras appear.
Google's justification for this (along with many customer comments) can be found in these blogs on this forum:
I know. The floodlight cams themselves are nice, but expensive. I purchased two of them on a $50 off Black Friday sale.
Mounting and wiring is easy, I mounted one above my garage and one in my backyard.
I like the fact that they can differentiate between, people, animals and vehicles and have face recognition, which my old nest cams do not.
I found a way to monitor them on my PC utilizing BlueStacks, an Android emulator. That will hold me over until Google finally gets the web version up and running.