With a solid class and/or ID hierarchy, it should be possible to override styles without using !important.
For example, to override a style for .wp-chatbot-chat-container ul.wp-chatbot-messages-container li, you could use .entry-content .wp-chatbot-chat-container ul.wp-chatbot-messages-container li or .wp-chatbot-chat-container ul.wp-chatbot-messages-container li.wp-chatbot-search-item. Adding these qualifiers before, after or somewhere in the middle makes the selector more specific, and therefore overriding.
I suggest you look through the superset of elements used for the chatbot and use classes that allow each element to be isolated for styling. Also, rather than using the prefix wp-chatbot, which is a bit long, and hyphenated, consider using wpbot, which also matches the plugin name.
And when you style things yourself, use the most general selectors possible, e.g. all paragraphs or all list items in the chatbot, as this will allow developers to override using slightly more specific selector.
After the last update, settings are saved OK, although this takes a while, and the font size from the settings takes effect, so I no longer need custom CSS.
I think this topic can be closed. Thank you for the support.