I also have the same problem with my new galaxy watch 42 mm.
However, I only got the notifications one time. I don't know how but it happened after swiped the screen several times until i reached the end and opened the calendar gadget.
Waiting for the solution
I've just had a call from samsung saying that they can't help me anymore as it's a 3rd party app and they can't even tell me if the watch is even supposed to receive WhatsApp notifications or not !!! They just said they won't help so now what ??? Thanks samsung you got my money but now your not interested !!
I solved the problem after alot of trials and error. Galaxy watch don't recieve any alerts if the phone is on silent mode.
I changed my phone to vibration mode. And it worked. Then, i set the phone vibration level to Zero.
Now I get all notifications instantly and my watch vibrates.
Yessss I've cracked it!! I went into galaxy wearable app on phone, go into settings and scroll down to galaxy apps and there were updates needed to be done, done those and it's worked since. So I now have messenger and WhatsApp notifications, happy, happy birthday girl today as it was driving me nuts 🤯😁 hope it works for you too, let me know 🤞