We've built a Chrome extension that addresses this (and just released it two days ago, 01/06/22)!

In fact, the use-case you are describing here is a need that we've experienced ourselves, and we support both static comments and live chat.

You can check it out the extension here:

https://chrome.google.com/webstore/detail/netvyne-extension/hdmpoglhdchngeiefpiaiilfeicjjfap

I'll share some background in this thread as well if you're interested!

Thanks @Abishek for connecting us!