Not necessarily Iris related, but I understand that the universal jar also installs sodium and fabric loader. But when I put other fabric mods like lithium and phosphor to the .minecraft/mods folder, none of them work. I verified it in my log files. Is it because the universal jar installs the fabric loader in a different way?

To use other mods, you have to select "install as mod". if you dont do it, iris installs a special loader which only loads sodium and iris.