If by "push" you mean sending notifications through 3rd party servers like google's Firebase, I'd like not to use it.
I was using XMPP on mobile for years, receiving messages in background normal way almost with no battery drain.
I also run k9mail 24/7 with my personal IMAP server, receiving messages in realtime (imap idle) with almost no battery waste.
Battery is wasted more by bloated frameworks like Electron rather than by network activity itself.
It's not activity itself but what app does in background in reaction to incoming packets. Clients I used (Bombus and Xabber) didn't support that XEP with no problem. App may just ignore some stanzas when not needed.
Mobile push is a combination of brain damage and bizarre propaganda targeting developers.
These days there's also UnifiedPush which is an open standard for push on Linux and Android. FluffyChat and SchildiChat (both Matrix clients) support it. I actually switched to SchildiChat from Element because Element's notification service was using too much RAM.
A lot of effort went into Prosody 0.12, which we released recently. It's unfortunate that mod_cloud_notify didn't quite make the cut for that version, but it was better than delaying the long overdue release even further. The vast majority of work on Prosody is unpaid volunteer time, and as with most open-source work there are certain kinds of tasks which are hard to find funding for, leading to the old "it'll be done when it's done" because we (the developers) simultaneously need to pay our bills.
Also, in recognition of many desirable things being in community modules, one thing we did prioritize in 0.12 was the plugin installer, which should make it easier for people to add additional modules to their Prosody installation.