How many people in the group chat? like 20 or 200?
If it's 20 people, you can try simpleX.  If it's 200, you want matrix.

Are people outside the organization contacting you for support?  If so, that likely rules out simpleX and nostr

Are you trying to hide the metadata? If not, could use someone else's matrix server, one of the public ones 

 Probably in the 50-100 range no support 

Just trying to get these people off volunteering IM data for AI based Intel machines 

 you'd actually probably be better off with Signal if you're not interested in running the VPS.
Signal can do private groups of 100