A tiny logo [as in just large enough to identify the plugin leaving the message, but not so large that it’s obtrusive] is a good idea.
I have logged into client sites that had 5+ notifications and one of them was important and from LiteSpeed but I did not know that as it didn’t identify itself and the error was a bit obscure.
These do look reasonable to me: https://www.screen-shot.net/2022-11-01_14-24-21.png
It may be that they scale larger if the message is not a single line?