While Matrix is decentralised, it's not considered part of the fediverse as it has it's own protocol and cannot federate with other decentralised platform.
But, personally, I don't think a fully federated chat/message platform based on ActivityPub is fully possible, or even a good idea
A few thoughts. You might want to look at the alternatives with https://alternativeto.net/ . The next question is to try to figure out what your privacy and security expectation is. Why I say that is that as soon as you share then things cannot be private. One has to think though in detail when is public and what is private. The fediverse is heavily public. So not sure if this is an appropriate Fediverse App. Maybe try to understand activity pub too and other fediverse apps. See https://en.wikipedia.org/wiki/Fediverse for a list of apps. I do not know the best activity pub intro.
Another direction. We do know that there are activity pub integrations for web platforms like Word Press, Drupal, and Hubzilla which are kind of general. One could perhaps have a secure forum that had some public fediverse interfaces for example.
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