Hello and welcome,
Is not quite clean looking, isn’t it? And quite generic information
Usually this is the kind of information we look for and the format to be provided be:
You mentioned architect install. Why not directly the preferred DE ISO ? That way you avoid most of the struggle or forgetting about some packages.
Each DE uses a default DM:
KDE PLasma > SDDM
Gnome > GDM
XFCE > LightDM
So, depending what DE you installed, the service corresponding to the DM can be checked if active or not. Example:
systemctl status sddm
Because i see zsh
and you mentioned Fedora, i can assume you installed Gnome. That means:
systemctl status gdm