It looks like I have FINALLY RESOLVED this issue for myself with a seemingly easy work-around. This involves simply installing Tasker. It's a paid app, but, given that it solves such an annoying problem for myself, it's definitely worth the small price.
It seems that in Android 11 only Ringer channel sounds are allowed to be played on BOTH an attached Bluetooth AND the phone speaker simultaneously.
To achieve "Notification" type sounds over both channels simultaneously first I copied (NOT MOVED) over the actual notifications sounds located in "Internal Storage\Notifications" into my Ringtones directory on my device: "Internal Storage\Ringtones". Now I can choose those same Notifications type Sounds as Ringtones.
Next I installed Tasker.
Since I have a separate Notification Sound for my spouse's text messages, I created a separate Tasker Profile for her Notifications:
"Received Text Any, %PNUM/Spouse" --> Task: Play Ringtone, Type: Ringer, Sound: Ding
Next, I created a Default Text Notification for all other contacts:
"Received Text Any, %SMSRF/!Spouse" --> Task: Play Ringtone, Type: Ringer, Sound: GoodNews
Then I even created a Notification to let me know the laundry was done:
Notification LG ThinQ --> Task: Play Ringtone, Type: Ringer, Sound: Piano
Hopefully this will help others as well.