Any way to push contacts to car kit?

[PhAndersson]

Hello again,
I was able to pair my newly installed Pixel 3a with the car kit of my Skoda Octavia, and I'm glad to report that everything seems to be working:

• I'm able to use the car sound system to listen to music played by the phone (selecting Bluetooth as source on the car Media Centre)
• the car displays the phone's battery charge and GSM network strength
• when an incoming call is received, the ringtone comes through the car sound system
• I'm able to take the call from the dashboard and the voice goes through the car sound system as expected

Now for the question: is there a tool that would allow me to push my contacts to the car kit over Bluetooth?

Thanks in advance.

Ph. A.