As said,
Using E25.4 on my latest Bookworm based Elive (crossgraded) machines, the notfication (for i.e system messages or news or updates available) are always there in two-fold.
One instance that contains the message which disappears again after a while and .... a pop-up showing the alert/notification icon which requires manual removal.
It looks as if E25 handles notifications differently to E16 (no surprise there) and gets the icons muddled.
. 
If you check your ~/.e16/startup-applications.list you will see an entry called notification-daemon, this is the notification used in E16
In E25+ you can still use it, but E25+ has its own notification e-module, so you are probably using both
Knowing that, you can try the one and the other, the default notification system has some features that are used in Elive like "buttons" so if we want to switch to the E25+ one we need to verify that all the features are correctly working, otherwise, we can report these "lacking features" to E issues
Example button:
result="$( el_notify wait znes "Title" "Description here" --action=open="button text" )"
echo "$result"
Standard features of the notification system:
~ ❯❯❯ notify-send --help
Usage:
notify-send [OPTION…] <SUMMARY> [BODY] - create a notification
Help Options:
-?, --help Show help options
Application Options:
-u, --urgency=LEVEL Specifies the urgency level (low, normal, critical).
-t, --expire-time=TIME Specifies the timeout in milliseconds at which to expire the notification.
-a, --app-name=APP_NAME Specifies the app name for the icon
-i, --icon=ICON Specifies an icon filename or stock icon to display.
-c, --category=TYPE[,TYPE...] Specifies the notification category.
-e, --transient Create a transient notification
-h, --hint=TYPE:NAME:VALUE Specifies basic extra data to pass. Valid types are boolean, int, double, string, byte and variant.
-p, --print-id Print the notification ID.
-r, --replace-id=REPLACE_ID The ID of the notification to replace.
-w, --wait Wait for the notification to be closed before exiting.
-A, --action=[NAME=]Text... Specifies the actions to display to the user. Implies --wait to wait for user input. May be set multiple times. The name of the action is output to stdout. If NAME is not specified, the numerical index of the option is used (starting with 0).
-v, --version Version of the package.
Good, I was hoping on a heads-up on this. I wasn't sure which one was used when and where.
I had a look at "el_notify" which came up like this:
So I was thinking it was the additional "crit" that did this.
BTW,
the top 2 commands pertaining "nm-applet" are what I need to do to get the icon to show in the systray.
I have to make sure it isn't running invisibly already ... else it wont show. 
You can enable / disable these two types of notifications system from:
I've disabled the notification module on E25.
I'll see what that does.
would that mean manually turning off the daemon, if logging out of E16?
I don't seem to be able to find that daemon, at all.
On a sidenote,
I seem to be getting 3 "authenticate" pop-ups every time I log in on E25 or E16.
reminds me of:
just kill the process or start the daemon, which is /usr/lib/notification-daemon/notification-daemon
something about permissions should be wrong on your system, try an over-install ? , can be the /etc/sudo* files or the sudo configuration or the aliases like "apug", which had a wrong update before (possible that referenced thread you said) that added the option -E which seemed later to fail
