Opening the codex with the corresponding key works and the menu is displayed. However, when trying to enter something, neither the entered text nor or any results will be displayed. You can still close the menu.
The English Minecraft Wiki was downloaded and all settings are on default.

The following error message appears in the console during startup:

[main/WARN]: Error loading class: fr/catcore/server/translations/api/resource/language/SystemDelegatedLanguage (java.lang.ClassNotFoundException: fr/catcore/server/translations/api/resource/language/SystemDelegatedLanguage)
[main/WARN]: Error loading class: org/jetbrains/annotations/ApiStatus$Internal (java.lang.ClassNotFoundException: org/jetbrains/annotations/ApiStatus$Internal)

Versions:

• Minecraft 1.19.3
• Fabric Loader 0.14.13
• Fabric API 0.73.2
• Codex b0.1.0

Error found!
It was my fault, I didn't get that you have to click on the field with the mouse.
But perhaps it would be more convenient to automatically select the field automatically when the menu opens.