There are some pretty unique programming skills involved but it might fall under the general rubric of "systems programmer" or a specialist in networking, e.g., you are probably writing servers that have more cross-thread or cross-fiber collaboration than the average webserver.

At a BigCo - sure, they have entire teams of dozens of people just for "messaging engineering" or "storage" or ldap/directory/identity, or email/messaging/telephony, etc.

It can be a bit mindblowing how many people are dedicated to seemingly mundane tasks at megacorps like making the phones work, making email work, making printers work, making sure the right people can badge in and out of the right doors at the right time, etc... all of which are not trivial at a megacorp scale.

Some years ago, I would say that this job title might have come under Middleware or Integration Engineer, or something like that, especially in big banks or firms like IBM. You might also try looking at job listings at a messaging vendor (e.g. Confluent).