“Nuclear powered” has no reference to their weapons capabilities, but instead how it generates electricity to run the ship.
Back in the old days, subs had diesel generators that required air to run the generators (like any fossil fuel powered engine) that recharged the batteries that powered the ship while submerged. That means that if the batteries were running low, the sub would need to surface to use the diesel engines to recharge the batteries so they could dive again. With the invention of nuclear powered subs, surfacing wasn’t needed except for replenishing breathing air. Which I think is like a few days or maybe a week or two. Or whatever, I’m not an expert on this.
Now, that’s not saying that a lot of nuclear powered subs don’t also carry nukes (like tridents, for example). But “nuclear powered sub” doesn’t have any bearing on that. It’s purely describing how the sub generates electricity.
I hope that any submariners that read this will correct me if I’m wrong. This is all based on info I read years ago.