As to battery drain, I'm sure it technically does consume more, but according to my phone it's an insignificant amount: <1% of usage which is the lowest stat it gives you. Their docs suggest the same thing:
> the app has to maintain a constant connection to the server, which consumes about 0-1% of battery in 17h of use (on my phone). There has been a ton of testing and improvement around this. I think it's pretty decent now.
https://docs.ntfy.sh/faq/#how-much-battery-does-the-android-...
Honestly it's a good solution that works well with few downsides, the only real one is that iOS doesn't support doing it, but personally I don't have any apple phones so I do get an essentially free lunch.
Notification and battery performance is on par with google's solution except when an android build does dumb things to prevent the background activity, in which case notification performance gets worse and battery draw gets worse (not sure why exactly, it's just a common issue in these regards).
However, it also isn't a big deal, at least in my experience, at least for ntfy.sh.