I hadn’t heard of Kate before, so I can’t offer much hands-on advice. I dug around and found a “handbook” here: https://docs.kde.org/stable5/en/kate/kate/index.html

Unfortunately it does look like you need to define a project to compile/run anything, which appears to require manually creating a .kateproject file in the directory as outlined here: https://docs.kde.org/stable5/en/kate/kate/kate-application-plugin-projects.html#project-create

I had exactly the same problem when I moved from languages that were interpreted or combined the IDE and runtime environment into one, and starting to use languages which had their own external compiler. Unfortunately, open source project user documentation is often terrible for beginners (what I found above for Kate seems to be no exception), and IDEs often seem to be written by people who don’t really expect anyone to actually use the included build options (to be fair, most folks seem to like using their own separate build utilities, so probably this is often the case)

If you can tell us which compiler or interpreter you’re using (e.g. gcc, clang, Python), someone can probably tell you how to compile and/or run a single-file program from the terminal with a fairly simple command.