I think not having just a bunch of pew-pew for the sake of pew-pew endless fighting has always been a part of Star Trek. When dealing with non-Federation space faring species, Star Trek shines when there is something going on other than just, “let’s fight.” I think the Klingons history with the Federation is a stand out, with them being on again, off again, frenemies. I wish that there was more exploration of the Romulans, but they too aren’t always in open warfare with the Federation.
TOS can lean a bit too much into offering peace, and then doing their darnedest to dismantle a society that slaps away the hand of friendship if that society doesn’t conform to Federation norms. TNG onward is much better at dealing with such situations. Not saying perfect, though – I’m looking at you “Symbiosis” (TNG s1e22).
I think TNG took some time to figure out how to respect the TOS framework without trying to be TOS version 2. “The Measure of a Man” is a standout episode. Where Federation standards aren’t just stated, they are examined and demonstrated.
I’m glad I’ve seen all of TNG, but I agree that the show more consistently finds its footing in season 3.