I recently (July 2022) bought a new Chromecast and could not set it up using my Pixel phone running the latest Google Home software. It kept telling that the device needed to be activated and sending me to a help page to download some Google Device Utility app which I couldn't find.
I eventually solved this problem by just setting it up from an iPhone.
This is something that the Nest team are aware of and depending on where you live the official instructions can be different.
Happy to hear that you managed to set up your Chromecast with a different device.