Hey there Sabz,
I'm sorry to hear that your new Chromecast with Google TV (HD) is giving you issues! I'd be happy to help you out, since I know troubleshooting screen mirroring is a bit tricky. Here is a list of prerequisite settings that you'll need:
Google Nest and Home speakers or displays and Chromecast devices might not be discoverable for mobile devices on Android 12.
During setup, your mobile device might ask them to "Allow Google Cast to use your network information."
Go to Settings Use network information Continue.
You also have the option to select Not now, but if you select this option, you can’t continue with setup.
Important: The Microphone permission in the Google Play Services app needs to be turned on to successfully use the Cast screen or audio feature with Chromecast. If you don't have this permission turned on, the Cast screen session immediately disconnects after it attempts to connect.
To turn on Microphone permissions:
I look forward to your response, and if you have any other questions or concerns for me, please let me know!