Is it bad SEO? Flashing, blinking, switching page titles from chat product

(Hi, guys, I used a few adjectives to boost this question, SEO-wise, as the best and most recent results are 2021.) My site has a chat function on its Home page. The browser tab flashes the "Page Title" of the Home page, then "\[New Message\] Page Title" of the Home page. Does it affect indexing? Does it affect usability? If it's detrimental, is there a common solution to remove that second title? Some setting or app that might force one over the other, etc.? RAJ