What phone and watch was that? It really shouldn't be a problem. You should be able to pair multiple bluetooth devices. My Pixel 2 XL and Huawei watch and
Android Auto are all paired and when I play music or navigate, I get that on my watch as well as the HU of course.
In fact, my problem is slightly reverse. Almost every time I get into the car, it prompts me that the contacts have been updated and do I want to update them. I have no idea why it thinks my contacts have been updated and why it keeps asking me to update them on the car. Even if it incorrectly thought that they had been updated, it should just have updated them without the prompt. One of these days, I'll get sufficiently annoyed to track it down.