All I can help with so far would be e.g. FCOChatTabBrain where you are able to setup keywords to notify on via sound.
If you enable the sound even if the game is minimized you would hear it.
But it does not provide any history nor notification entries (and they won't get added).
And check out this addon:
https://www.esoui.com/downloads/info2893-ChatAlert.html
Not sure if this whisper notifications of the addon are causing the task bar to flash as well, you'd have to try this.