Yes. Unfortunately, Google Nest decided to have its new Google Nest cameras and doorbells--the ones released starting the fall of 2021--work ONLY in the Google Home app and NOT in the Google Nest app or on the home.nest.com website. We've had a Google Nest Camera (Battery) for 10 months and have had to use 2 apps ever since.
Google Nest's Vice President posted this back on Sept. 29, 2021; there has been no update since:
Thanks for your assistance, MplsCustomer.
Hamiltom, thanks for reaching out! I understand that you'd like to set up your 2nd gen Nest cameras to your Nest app, however they can only be paired in the Google Home app and you can view both your 1st gen Nest cameras and 2nd gen Nest cameras in the Google Home app. For your guide you may check this article to learn how to set up your 2nd gen Nest cameras.
I hope this helps.