Booting Chromecast requires working Internet with unhindered connection to a Google server with a non-fake TLS certificate. So using Chromecast seems to be not an option in my use case.
What else can be used to cast screen / audio from Pixel 3 to some HDMI-outputting device? Are there alternative hardware devices that are compatible with Pixel 3? Can [rooted] Pixel 3 running Android 9 use Miracast instead with some third-party software?
Or maybe there are some other methods to make a "virtual Google" to allow Chromecast 3 to activate?