We have missed so many live chat messages - when we used Tawk.to it would ring like a bell whenever there was a live chat waiting. For a small company like ours, we only get a few chats per week so we're not always looking at it.
Totally agree, I am also waiting for the customization of the notifications, and sound notifications, of the search engine. While waiting for these features, I advise you to install the Pipedrive mobile application. It allows to have a sound notification and/or vibrations, etc.