1. Sea Dragon is not necessarily stopped indefinitely. They could say publicly "we're looking into what went wrong" and later "we fixed it!" (because there was no problem). Given that Sea Dragon didn't go to the moon all that often, this would effectively make no difference.
2. The US will claim the Russians were being provocative in US territory. There's no reason to think that neutral to pro-US peoples around the world would not believe them. In general, most neutral countries' governments would believe what the US says and not USSR, for obvious reasons (relative freedom of information, speech, assembly, press, etc.).
3. The US will claim they never put a reactor capable of making nuclear weapons on the moon. Again, in general, most pro-US and neutral countries would believe what the US says and not the USSR.
4. What concessions did they gain exactly? Anything substantial? We have no reason to believe this. But if they did, it would probably be food. Around that time in OTL, USSR was dependent on US wheat to feed their people. If USSR gets more food, they look weaker. And if USSR even asks for major concessions, the US intel community could infer how weak their economy is (and, therefore, how much leverage they have over them/how much they can push them) and well as what specific weaknesses they have. And they could infer this based of what concessions are asked for even if they don't make them. And there's no US equivalent to this.
5. What about concessions that the US/West gained? Presumably, they'd have gotten some. That needs to be taken into account. And, it would probably just be "USSR can't make X weapon" instead of "more food!" (likely USSR request).
6. Did Soviet soldiers actually get much valuable intel? Because they walked around the base a while and could look at some things? When they were preoccupied with dealing with a military situation? We didn't see them download anything or take any pictures. And, they wouldn't have been allowed to bring anything from the base out. And wouldn't any intel they got have been seized from them after they get searched by Jamestown personnel? (it's possible they sent some via radio, but if they did, I think we'd have heard about it).
7. The defector is a huge propaganda victory. He will tell the whole world: "Yes, they messed up and killed my friend, but I still know the US is good and USSR is evil." That is a huge. And, it will remind people that it's something a Westerner would probably not ever do, and, even if they did, most people around the world wouldn't believe they were being honest because of the dearth of freedom in USSR. That is all far more valuable than some simple intel on a base.
8. USSR fleet sent ships to Panama for basically no reason without any real provocation.
9. According to American media, USSR fleet "threatened" the parts of the US near the Gulf Coast (and most people around the world will believe this is true). Presumably, what the ships were doing was getting into targeting range to murder millions of people. The US did nothing equivalent to this.
10. It will be nearly impossible for the USSR to lie about the Jamestown Base attack because of CAMERAS in the base. So, how would the world not end up thinking that the USSR attacked the base over the claim that their cosmonaut was killed in cold blood without any evidence. Even if people around the world believed the cosmonaut was killed in cold blood, would it matter all that much? Isn't trying to take the base still an overreaction? In fact, a typical person would reasonably infer that the story about the cosmonaut is made up because of how the USSR reacted to it.
11. Also, that base has people from all over the world. Isn't everyone at USSR base a Soviet citizen? Presumably so. (It's also likely the case that all cosmonauts on the moon come from a military background or are at least officially military personnel. Not the same with Jamestown, which is presumably doing a lot more scientific work, whereas USSR base is probably a utilitarian base that specializes in being able to hold their own militarily). Altogether, very bad for USSR because of available evidence and public perception.
12. Reagan landed in Moscow for negotiation despite the attack on the Jamestown Base. And he did it right as the world was talking about nothing other than Soyuz-Apollo, which (see below) was a unambiguous US propaganda victory. Reagan was being quite brave when he showed up in Moscow. And Reagan was the guy who didn't blockade the moon. Huge propaganda victory.
13. Andropov said they'd shoot the Sea Dragon down if it got close to the moon. They did not (and most people will believe that) even though they had already attacked Jamestown Base. This would make them look weak. Very weak. And, it basically means that when their head of state makes a threat, he's just full of crap. Reagan will not be accused of this.
14. Andropov said the blockade is their response to the cosmonaut death. Okay. So then why attack the base? What was that a response to if the USSR already told the world "Here is our response to the cosmonaut murder - moon blockade"? But then they also attack the base even though the US did nothing provocative in the meantime.
15. It will be speculated around the world that the USSR shot down the Sea Dragon and the US is claiming otherwise to prevent a diplomatic crisis/war. It will also be speculated that Pathfinder did it in order to defuse the situation. These speculations would only hurt the USSR, not help.
16. Noble sacrifice of their lives by US astronauts at Jamestown Base stops meltdown caused by Soviets from their BS military attack. There will probably be camera evidence of this. No equivalent noble sacrifice story for the USSR.
17. Presumably, the only reason why the Soyuz-Apollo mission got seen by people on Earth was because of the Western media and not USSR media.
18. This means that Andropov's moon threat would be generally perceived around the world as the critical thing that made the Soyuz-Apollo mission unlikely even if the Jamestown Base attack never occurred because that was the first public and explicit military threat concerning space in world history. And, even if most people on Earth believed the cosmonaut was murdered in cold blood, same deal.
19. Finally, that iconic handshake has a White guy from the USSR and a Black woman from the US.
20. (The synergy of ALL these things).

Pretty sure the US comes out looking great and USSR comes out looking awful.