Thanks MoonJ for trying to help. I was at Google community and no one seem to have an answer. There were thousands of people with the similar issue and hudgreds of posts.
I found the solution and reported to Apple senior advisors, who tried to help. It took me at least 5-6 hours, to find that all it was just one setting. Here is what I found:
In the settings, navigation turn "Access your Assistant with OK Google" OFF! That made my car speakers connected back to my iPhone, Google map through "Play as Bluetooth phone call." Possibly this is the main reason why I was never be able to use Waze through the car speakers, has the same on and off google assistant setting.
P.S. why this started happening after installing iOS14.3, which was mentioned in the original post. Because I reinstalled the Google Map and the default setting is have the Google assistant on, which shots up SIRI commands and not able to connect to car speakers. It says right thwere in the settings.
Happy Holidays!