I suppose it depends on what you mean by server and client, I only use the web interface, so my client is the server? :)
Fediverse is built on ActivityPub protocol, which allows people to send content around as they wish without limits on exactly what sort of content it is.
So it's really up to different programs like Mastodon, Pleroma, and whatever else to work out what to send around and how to render it to the screen.
Third party clients do add yet another layer to that, though.
I believe the message is somehow tagged as to whether it's markdown or not.
After all, when the website displays markdown vs text, it somehow knows which way to go.
Apps should have the same opportunity.
And this doesn't require any sort of browser plugin. It's just a webpage.
Could this best be accomplished server side or cliënt side?
Really dont know 😏