I'll try to add on to what others have said. Matrix is a protocol. Element is the client made by the people behind Matrix but you can use any Matrix client. Matrix is the protocol behind Beeper but they don't put much effort into integrating with Matrix, so for example (last I checked) you can't log in to a Matrix account on Beeper.

However, your Beeper account is a Matrix account so you can join Matrix rooms with it. It's a little janky, but basically you go to the menu in Beeper and find the option to join a Matrix room, then follow the instructions. From memory you might only be able to do this from the desktop application, not on mobile, but the room shows on mobile once you connected on desktop.

Lemmy.NZ has a Matrix chat, see: https://lemmy.nz/post/169187

There is an NZ homeserver: https://mtrx.nz

This is run by fediservices.NZ, the same folks who provide a server for us to run Lemmy.NZ on. But you aren't able to connect a matrix account like this into Beeper, you'll need to use a different app like Element.

Hope this helps!