Ok... let me start by saying that I'm not trying to tell you what to do, just that I don't think those arguments are all that solid.

The topic was to coordinate in case of an attack, so you'd probably want to verify identities and avoid imposters, which Discord "kind of" does through things like its integrations with other ID services... but there's nothing like a good cryptographic signature. Discord has a "report raid" option for a reason, it isn't bulletproof.

how to set up a matrix server that is invite only with one link instead of having to invite them all one by one?

Maybe.

A whole server, can be done, but why? A private space, or private room... I guess you still need to use a bot to invite from a link.

There are some bots out there with other interesting features though, like a "knock" option to let admins/mods know of join requests and accept/reject, or a setup where they use two rooms: one public, for everyone to join, with a bot that you can ask nicely for an invite to the private one.

Strictly speaking, all Discord features and more are possible via Matrix bots... but probably not yet available through a user friendly GUI, if that's what you mean.

which one is more popular

Nowadays, either is a click away; whether the web UI, or some app in an app store.