In my experience, no. I keep getting calls from my elderly dad, but the notification level can be dialed up or down - in my case, I get very few spam notifications. Put it on DND and it's almost zero.

If you happen to have full notifications on for slack/Facebook/etc yeah it can get annoying - but you can't really immerse yourself in it.

I think of the watch as a pure comms/notification device whereas the "phone" has become a full-on handheld computer.

I'd say it is alleviated quite a bit actually because it solves a corollary issue. To me personally, the majority of the issue is in the magic box that promises me instant dopamine any time I pick it up and turn on its screen. I don't mind getting a message and choosing to respond. I do mind, however, being tempted to open any of the attention seeking apps or websites after I'm done with my message or call. The watch has virtually none of that temptation. YMMV depending on whether the notifications or the decision fatigue are more of an issue for you