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As stated in the previous article, you may also use PSR-7 for AJAX requests. However, the implementation in the backend and the frontend is different. This article explains how you setup so-called "routes" for backend AJAX requests and how eIDs look like for the frontend.
Ah, you have a non-extbase extension whose content is cleanly structured into Classes, Configuration, Resources, etc. But then there are these pesky modX/index.php files for your backend modules. That's not nice, but there is help: PSR-7. This tutorial shows how to setup your backend modules according to PSR-7.