Is there a “modern” equivalent to XMPP? How does it compare to the matrix protocol?
Let's use group chats as an example: with Matrix if you join a group chat hosted on another server, the entire history of the chat gets synced to your server. This means it's very resource intensive to scale, but very reliable since you pretty much always have chat history available and if one server goes offline you can keep the group chat alive on one of the other servers (let's ignore netsplit style concerns for now, it's not really relevant to the high-level nature of the question). XMPP on the other hand is event based, this makes it much less resource intensive, but means that if the server you're trying to communicate goes down you don't have access to that chat room anymore (some servers mitigate this by using traditional high-availability techniques like clustering, but that's not really a protocol thing, I'm sure some Matrix servers also do clustering as part of their scaling strategy).
As far as features specifically related to IM, both support most of the same things, it's just a question of whether clients have implemented them or not in either protocol.
I am still aware of both protocols, I still don't like Matrix and think XMPP is "good enough", or at least the best choice. Having an opinion doesn't make me biased against one or the other.
Not being paid for the work on something doesn't imply no bias towards it.
> Having an opinion doesn't make me biased against one or the other.
It might: Confirmation bias
> with Matrix if you join a group chat hosted on another server, the entire history of the chat gets synced to your server.
This is not true. By default most Matrix implementations sync the last 20 messages in a room when a server joins that room, pulling in other messages only on demand if a user back-paginates the room. Room state (i.e. key-value metadata about the room) also no longer gets synced in atomically at join - instead it gets pulled in in the background (so-called 'faster joins': https://element-hq.github.io/synapse/latest/development/syna...).
Yes, it's called "XMPP".
XMPP continues to advance, so could be considered modern if you use the latest versions.
Matrix is more of an event sync protocol, consisting of a server to server sync protocol and a client to server protocol (sort of like email). It is mostly used for chat, but appears to be more flexible. Matrix uses JSON and HTTP.
XMPP is focused on chatmessages. In many ways XMPP and Matrix are similar. XMPP is based on XML and originally used TCP as the transport protocol, but has been extended to use HTTP now as well.
EDIT: I think a clearer way to describe the basic difference is that Matrix syncs Matrix Events across servers, whereas XMPP facilitates exchanging messages with clients. Most folks use the protocols to exchange chat messages. It is the way this is accomplished by the corresponding servers that differs significantly.