Sadly aria-net is down quite often, and in general the "Bifrost" bridge that is uses is apparently a hard to maintain mess of spaghetti code. I can't recommend using it for anything important.
There is a new work in progress gateway built into Ejabberd, so if you are self-hosting that, it can be used to contact people on Matrix (but not the reverse), but it seems to be more of a proof of concept right now.
Last but not least there is a Matrix gateway build with Slidge that you can self-host. It connects to an existing Matrix account and even does e2ee (but this ends on the server where you have Slidge installed). This is probably the best option right now, even though the codebase is still in heavy development.