Unified push is great news in general for AOSP based ROMs phones for battery life, it's an open notification standard and system. There are several providers or distributors. If you're already using nextCloud with the unified push support on the server (murena has enabled this already because they want apps to consume less energy because of having to run in the background if not wanting to use the proprietary google services notifications) then you can use the unified push app already available on f-droid. If using conversations (xmpp client) it already supports working as an unified push provider and perhaps other xmmp clients already added such support and conversations is also available on f-droid. Or you can use the ntfy provided app also available on f-droid. There's an apps list available to find out if particular apps already support unified push, and as you can see fennec is one of them. BTW, if one doesn't want or need push notifications on fennec this can be disabled on its notifications settings, When installing an unified push notification provider, the apps supporting it will attempt to subscribe with a particular topic name on the provider, and usually the providers come with default settings to automatically accept subscriptions, and one can just check if the subscription is there already or not, one might need to stop and re-open the app for it to attempt to subscribe. Make sure the provider is running in the background without restrictions, I can tell conversations and ntfy are pretty low battery consumers so no worries about no restrictions on battery consumption.

Does that help? Otherwise I'm kind of lost with the questiosn.

I tried to find unifiedpush on fdroid and even play store, no dice. Found sunup which says its a mozilla unified push so seems right. Now fennec is complaining about unified push and sunup is saying waiting for registration to connect. Lol