2 is BS with capital letters. See Converations and it's forks.
Did you ever wonder why there are no (to date) XMPP clients on iOS that are not complete and utter shit?
As a person who has first-hand knowledge of the matter, managing a team member tasked with the development of an iOS XMPP app (which is supposed to be NOT complete and utter shit), I tell you that creation of such app is impossible without reinvention of half of XMPP stack (basically every part that touches client-server interaction). Thankfully, s2s works rather fine in XMPP.
To counter this and make XMPP work well on mobile and in browsers, we had to develop our own server and a bunch of new protocol extensions.
XMPP server -> Push service -> APNS / FCM -> XMPP client.
Push service here is a service maintained by an XMPP client developers, cause you need a client app certificate to be able to send messages to it via APNS/FCM, and no sane devs will be handing out their certificates to third parties.
It should be noted, that the recent changes to how Apple push notifications work in iOS 13 (MORE restrictions on VoIP and 'silent' background notifications) require some updates to it, but so far, XEP-0357 does not look like something terrible.
