Luxchat4Gov and Luxchat for the general public and businesses are interoperable national instant messaging services, based on the Matrix technology.
Matrix is an open standardized protocol for instant communication, developed by a large, mainly European community, and supported by a foundation, The matrix.org Foundation, guaranteeing the sustainability of the key principles and foundations of the Matrix technology.
How ready is Element for the general audience?
I use Element daily, and it can be confusing enough that average users would probably stop using it when they have to choose a server, or when that server have issues with images, or when they can’t read a message because the room is end-to-end encrypted but they need to reverify another person’s key.
For the context, LuxChat is the general audience version of LuxChat4Gov, a fork of Element created by the Luxembourgish government for the public servants: https://mindigital.gouvernement.lu/fr/luxchat4gov.html (France has a similar app with https://www.tchap.gouv.fr/ ). The objective was to provide public servant a messaging app that would not rely on Google, Apple, Meta or Microsoft.
LuxChat and LuxChat4Gov are managed by LU-CIX Management G.I.E. G.I.E stands for Groupe d’Intérêt Economique, which is not a company
https://www.fiduciaire-lpg.lu/fr/publications/droit-des-societes/le-gie-groupement-dinteret-economique
If you look at the composition of LU-CIX, you can see different types of entities, including the CTIE (Centre de Technologie de l’information de l’Etat), which is the IT Service of the Luxembourgish government.
https://www.lu-cix.lu/about-us/lu-cix-management-gie/
On a public perception level, LuxChat is targeted towards companies and individuals, and is backed by the government. If you are a Luxembourgish company and are looking for an alternative to Whatsapp, are you going to trust more an app backed by the Lux governement, and that has been reworked to make it easier to use, or Element, for which you have to trust a server anyway, and figure out how it works.
All your concerns remain valid from a technical perspective. The people behind info-luxchat[at]lu-cix[dot]lu may have some answers.