Most of the UI components on the $chat_support page cannot be customized. It is an angular page which has most of it's components hardcoded in the backend. This includes the .js and .css files which control elements such as font, background and modals/buttons.
It is possible to change the system's theme which would affect the $chat_support page as well, however this change would be a system-wide effect.
Below is an example of how UI macros can be accessed to modify some out of box texts that appear on the modals.
Please see KB0696863 as an example of how texts can be modified on the pop-up modals that are part of the $chat_support page.