I don’t see anything in that article that says that Google store the contents of the notification. It just says that they link push tokens to emails, which is true - they have to know who to send the push notification to.
In any case, if you don’t want Home Assistant notifications being relayed through Google, you can use a persistent connection so that the app connects directly to your Home Assistant server.
You can enable a persistent connection to get alerts directly without relaying them through Google, but then you need to have a connection to your Home Assistant server all the time (eg by using a VPN or by exposing it publicly)