Google doesn't have any magic way to do instant notification that nobody else has access to. The only thing they have access to in this regard is disabling any battery optimisations without triggering warnings.
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).
Well, there is an advantage, if everything is using the one service then you only need to have one thing alive to check it, so each new app is "free" if you already have push enabled (assuming that push notifications are rare enough the activity isn't the cost), as where each app doing it themselves is going to cause more battery use, so it isn't directly equivalent.
However, it also isn't a big deal, at least in my experience, at least for ntfy.sh.
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).