I wouldn't get to concerned about bringing dressy/formal attire for evening wear. Unless, of course you choose to. LOL
I have been on NCL and Celebrity since we resumed cruising and saw very few people dressing up. Both cruises were to the Caribbean, and I don't recall seeing one single guy in a suit. Some sport coats, but mostly nice pants, short sleeved shirts and Tommy Bahama like shirts. Ladies in skirts, capri and nice pants.
I've been to Alaska twice, once on Celebrity and the other time on RC. And most in the dining rooms wore very casual clothes. Mostly jeans to be honest. Although that was quite a few years ago, I am guessing it is still the norm for Alaska.