for me (and other users what i read in articles i can't find right now) it asked me in the google home app to activate the connection to gemini as soon as it's available (which isn't right now).
so i assume after this it should work, if you already connected your home assistant to google and are able to control devices via the google home app.
i tried the other side, connected my gemini to ha's voice integration which enables me to control everything via AI (which works really nice, but is not the way i want to use it, or, i'm just trying out with a satelite device i recently bought, but the performance is a bit weaker and it's responding slower as a google home speaker, which makes it unusable for me actually). but it's nice to be able to ask "which lights are turned on", "how are the temperatures in my home" and so on - so i will wait until it works, think everything should be good then.