The pizero won't be able to run a matrix server most likely, but if you want you try anyway, use conduit.rs (matrix server that is more lightweight). The pizero probably wont be enough

A Pi zero is really underpowered. You might barely be able to run a XMPP server with a Slidge.im bridge, but Matrix is definitely a no-go on that hardware.

I don't have any experience hosting matrix but I think it is quite a stretch for a pi zero.

Matrix's official homeserver synapse is written in Python which is not known for resource efficiency. Adding in bridges does not make the situation look any brighter...

On the other hand, Pi Zero is powered by a single ARM6 core and merely 512MB RAM. ARM6 has been losing support due to its age and (lack of) performance. You may have a hard time setting the stage up. You may need to compile a bunch of packages from source which will likely take forever given the single ARM6 core. Also 512MB RAM is real small and you cannot have them all as the OS also needs RAM.

You can give it a try. But I bet it will be quite a torture.