the missing bridge is still a Nextcloud push mechanism itself. Despite its name, nextpush isn’t it yet - Add UnifiedPush to /e/OS to make it possible for developers to avoid FCM and better support F-Droid applications - #21 by tcecyk
While Nextcloud has an app to be provider, Nextcloud itself doesn’t yet support pushing to a UP provider. Seems to me it’s more likely to arrive with supporting WebPush
more Nextcloud + push discussion is at https://github.com/nextcloud/server/issues/22379