Antoine
Andoine, many differences between Vscodium and Kate are to be expected. Vscodium is an Integrated Development Environment, or IDE, and Kate is the KDE Advanced Text Editor. You'll typically find a lot of features in an IDE that are not in an editor.
I don't use an IDE on Linux, but it sounds like you just don't have Codium installed properly. I might be able to help you with that, but I need some answers from you first. Are you working on a school computer or your own at home? Since Kate is part of the KDE suite, I assume you're using Solus with the Plasma desktop. Is that right?
Did you use the Software Center to install Codium, or did you use the eopkg package manager from the terminal command line? If the latter, what command did you use in order to install Codium? I'm surprised that you could find the auto-completion feature in Codium if it's not installed right, but I'll try to help.