Sending a text in the chat and trying to "click" the button using requests sessions. Python

So I'm trying to click the button using requests sessions. Keep in mind, I don't use Selenium for some reasons. The button posts some kind of Yandex pointers, but I can't seem figure it out what are they doing. Sending, submitting a text in the chat also posts pointers, I have got no idea how the text is sending through. Buttons aren't providing any information I could use in my code (HREFs and etc). The website I'm trying to automate is https://runechat.com ; I would appreciate your help!

Button HTML code: link

Button POST data: link

Chat button HTML code: link

Chat button POST data: link