With Firebase, the reported battery consumption is 0% obviously. Without Firebase (i.e. with the instant delivery option) it varies depending on phone and usage. On my phone it is usually around 0-1%. Others that use it to deliver their Matrix chat messages have reported higher numbers up to 12% (though that is rare).
If you "allow background services" for the app, Android will kill it less often. Though some manufacturers are quite aggressive even with that option.
As for who pays the bills: The public server is run in EC2 ($25/month, though it could run on a much smaller instance), and the Apple developer license is $100/year. Other than that, there are no costs. Up until a month ago, i was carrying all the costs. I have recently started accepting donations, and now all the costs are carried by my awesome sponsors (see https://github.com/sponsors/binwiederhier)
More details:
https://ntfy.sh/docs/faq/#why-is-firebase-used
https://ntfy.sh/docs/faq/#how-much-battery-does-the-android-...
If you do use the Google/apple push notifications, who pays the bill for those?