This is correct, but it is still a slippery slope. At some point the dev ends up adding internet permission (might be for legit reasons too), and lo and behold you are sharing your data. For something as sensitive as notifications, I really can't trust anything but open-source app which is vetted by a few seasoned people and hosted on F-droid.
Also non-GrapheneOS Android. I'm on CrDroid (Android 16), ans if I go into "Settings -> Apps -> Some App -> Mobile data usage", there's a toggle for "Allow internet access", and a few more to control network access on Wi-Fi, cellular, background, and VPN.
Would a safe alternative (albeit annoying to update) be to side load the apk for the purpose of eliminating the possibility of auto updates brought on by an app store?