How to customize an online consultant for an online store website?

Question

1C-Bitrix

There was a task to make an online consultant for the website of an online store. The site is powered by Bitrix.
As I think, such an online consultant (chat) will be easier to implement on the basis of the “live site” widget, you need to customize it for their design, so I wonder if there are such opportunities to change the design of the “live site” widgets. The customer wants to customize the chat to the design of the site as much as possible.
Screenshot of the layout design - joxi.ru/5mdNBGnSk06QzA this is how the online consultant should look like.
Advise which services of online consultants are suitable for such a task? Where is it possible to change not only colors but add buttons, customize the style of the inner window, and so on?