Notification Channels is the official way to do this on Android, but it's up to the app developer to categorize them properly. They have no incentive to allow you to turn off ads.

If you're on Android, I'll always recommend Buzzkill to add very granular rules for notification filtering. I set up all kinds of filters just for the Amazon app.

On iOS I assume you're sol, that notification system is unhinged to my eyes.

I just turn off all notifications for any app that sends me marketing notifications.

That would be nice. I wouldn’t be surprised, as on-phone models get more capable, if we don’t see them start to build an “inbox” like we see with email where you can then start seeing much more heavy processing happening.

Too bad about the walled garden or you'd have this tweak already installed years ago.