This is pure speculation but,
Bluetooth isn’t a protocol in the strictest sense but rather a suite of protocols called “profiles.” A given BT implementation on a device can support some, all or none of these profiles. This makes sense if you think about it; it’d be nonsensical for a microphone to accept BT connections from a printer.
There are a number of profiles which cover hands-free car kits. You may remember in the early days having to choose between confusingly similar options like Hands-Free or Headset when pairing; you’re actually selecting different BT profiles here.
Now, it’s possible that your car stereo supports the correct profile for basic hands free (HFP) but WhatsApp is trying to use a different profile which isn’t supported by the stereo. I’ve had similar myself trying to stream audio on my old Mondeo; hands-free worked fine but music requires the A2DP profile which wasn’t included in the BT stack on the Mondy. If WhatsApp calls are stereo that’s probably the issue.
If I’m right, then there may be merit in seeing if there’s a firmware update for your head unit. Other than that, you’re probably stuffed. Or, y’know, I’m way off the mark.