Hey there and welcome to the Samsung UK and EU Community Forum
Your video (at the point of me commenting) isn't yet approved.
You don't need Android Auto to connect a Samsung Mobile to a car's Bluetooth stereo. So that isn't the issue.
The pairing number box is usually only on for a few seconds. So when you try to connect, click pair on your car stereo and see if that enables the connection.
I am not employed by Samsung nor do I receive any remuneration as a Samsung Members Star.
My device is an S25 Ultra.