Ultimately, i want something that is able to work outside of its own walls. I dont want 10 messenger apps, and i dont want to limit the messenging app that i host to just us (ie, it would be good if my account can talk to others, by my sons can only talk with us).

The funny thing about XMPP is that this is exactly where it started at, when AIM, ICQ, MSN, Yahoo and co. were all the rage in the late 90's, the geeks became annoyed of needing as many clients as there were protocols, and XMPP was meant to bridge over to all of them. Fast forward, we since learned that bridging to other protocols generally sucks (or isn't to be recommended to the average folks), and just to make sure, Matrix tried again 15 years later with the same outcome. But if you need it, the capability is still very much there and some still pursue the effort to this day.

Do you have any links for the french dropping matrix?

I only have a (private) IRC chatlog which I'm not sure it is ethical to post in the open, so I sent it to you by private message instead. I don't think it is a secret at this point so there might be other sources out there to corroborate this.