this is not tmux specific, basically every terminal out there would react to the bell char. e.g Terminal.app adds a bell icon to the tab, makes the dock icon bounce, and a badge on it.

if you want to hack a bit and have a specific log line outputted yo the terminal you can stuff the bell char right in the string!

one could also display notifications, there are more advanced CLI programs but here's a crude way: https://apple.stackexchange.com/questions/238814/send-notifi...

These things can also be done on Linux. A bit of web searching should give you ideas.

I frequently use them with long running commands or fswatch.