Develop a chat UI that is independent of XWiki and can be embedded in any application

Based on the library implemented as part of LLMAI-53, a new chat UI should be developed (most likely by refactoring the existing code) that is independent of XWiki, meaning that it uses neither JavaScript nor CSS code of XWiki. It should be usable by including a single JavaScript file and specifying some configuration (like where the chat UI should be displayed or how the XWiki server can be reached). The existing JavaScript code should be refactored to add any XWiki specific features on top of this new chat UI.