This is precisely why I haven’t purchased a smartwatch. These devices decrease our ability to solve problems that require analysis for extended periods of time.
I feel the same way. I found it interesting that when smartwatches came out, people were excited about being able to see text messages or other notifications on their wrist.
As someone who felt the need to be on top of things, receiving notifications was slightly stressful as it meant something I'd have to evaluate and make a decision on "right now". (Obviously, feeling like I should react to things immediately was something I had to work on in myself, but the phone didn't help.) Feeling a notification buzz on my phone gave me slight anxiety as I'd immediately react with, "oh, what is this that I might need to take care of?" Putting the phone aside for periods helped, so the idea of not being able to escape it with notifications on my wrist was a little terrifying.
In the last few years, I've set my phone to always Do Not Disturb mode, so it doesn't vibrate or even light up when a notification comes in. I do the same on my Mac. It's helped quite a bit with my stress levels. I just manually check periodically to see if there's a notification instead of always feeling like it could go off any minute.