Has Trump taken the hard right turn toward Russia and away from NATO he advocated during the campaign? No, but he has tacked in that direction. Our relationship with NATO countries has deteriorated from where it was. That's only a positive for Putin.
It's not that simple. First, our NATO allies aren't a monolith. I would say our relationship with Germany is worse. Ditto for France and the Netherlands but not anywhere near as bad as many expected. Emmanuel Macron surprisingly gets along with the Administration pretty well. It also helps that he has turned out to be a much more conservative President than most expected. The UK? Mixed bag. The rest of Western Europe? Not much of a change. Eastern Europe? Our relations are probably a little better than they were.
Second, I think we have to ask what big change in our foreign policy has caused Germany and to a lesser extent France to be less favorable to us. If you asked a Trump-hater in Paris or Hamburg to answer that question, he couldn't tell you much in specifics. He'd call him a racist, bigot, sexist, xenophobe, etc., but for most, that would be the extent of it. The real source of Western European hostility to Trump is differences in style and worldview, not specific policy. They're not going to be fans of a brash, assertive, trash-talking white guy no matter what he says or does, because their white guys aren't like that. They're also not going to like a guy preaching national sovereignty when their worldview is centered on surrendering one's national sovereignty. That's the whole point of the European Union, and those countries are where the EU is most popular, because they are the countries that most benefit from it. Nevertheless, despite the differences, a big part of our buildup is happening in Germany. None of that would be happening without the cooperation and support of Germany.
Third, have we really tacked in the direction of the campaign? Well, Trump walked back the dumbass "NATO is obsolete" remark, fired the people who liked that comment, and we've engaged in a military buildup (including missile defense) in Europe that is under NATO command. It's hard to see that as tacking in the direction of the campaign. It's more of a flip-flop. Let's put it this way. Musburger (and therefore Putin) definitely liked "Campaign Trump." They don't like what he has actually done with NATO and Europe.
We allow NK to be a major distraction. Win for Putin?
To be fair, NK has been a pretty big distraction for quite awhile - at least ten years, and I'd argue more like twenty. Does Putin benefit from that? In a way he does, but like China, he doesn't necessarily benefit from tensions really boiling over. He'd rather they just fester.
If anything, I'd argue that Trump's foreign policy has been inconsistent. There are some areas he's been good and deserves credit. He is getting Europe to think about it's own defense a little more which isn't bad.
I'll actually mitigate Trump's credit on this. Yes, Europe is pitching in more for its defense, and that's a good thing, and Trump and his people brag about this as if it's an accomplishment. However, this process was already well underway. There's no question that Western Europe cut their defense forces far too much after the Cold War. They bought into "The End of History" crap too much. However, the terror attacks of the last several years coupled with the Russia's aggression and its own military buildup changed their mindset quite a bit, and most of these countries started reversing their defense cuts a good 3 - 4 years ago. It has a lot more to do with their own reassessments of various threats than anything Trump or anybody in the US has done. And to their credit, both the Bush and Obama Administrations pushed them on this, albeit more quietly than Trump did.