I would argue more that anyone grabbing this from the app store is painting a target on their back. It doesn't matter what permissions it does or does not have: You are now giving a mega company run by a c-suite that have demonstrably bended the knee to a fascist information that you care about this.

Push notifications are incredibly valuable. I still argue that doing it through a dedicated app at all is idiotic and it should instead be through a semi-anonymous chat system like Signal or Matrix and the like and get group blasted.