Unfortunately, Google Nest decided that its new cameras and doorbells released starting in 2021--including the new floodlight camera--work ONLY in the Google Home App and NOT in the Google Nest app or on the home.nest.com website. Your floodlight camera SHOULD be installable with these instructions: https://support.google.com/googlenest/answer/9293657 (for the camera) and https://support.google.com/googlenest/answer/11003780?hl=en-GB (for the floodlight).
We've had the Google Nest Camera (Battery)--a similar device--since Sept. 2021, plugged in with the optional power cable. We're now stuck with having to use 2 apps (and it has fewer capabilities because it doesn't work in the Google Nest app), but we did not have problems installing it. When you say "not found" and "not connecting", what exactly do you mean? Was your iOS device close to your camera during the install?
Thank you for your feedback on this issue, I fully understand the frustrations of not having your new Nest Cams in the Nest App or available on https://goo.gle/3A7x7ug web app. I can imagine having to use two different apps at the moment is quite daunting, and could lead to frustration.
However, the new Nest cameras and doorbell are exclusive to the Home app because we wanted to create an integrated experience with your speakers and displays. A Nest Aware subscription applies to all of your cameras, speakers, and displays in the same home structure. Thank you for your continued patience, and support.