Personally, I don't think the movie is offering any easy answers about anything and that's kind of the point. It is a film mostly told subjectively through Oppenheimer's view, and therefore the whole film is an exercise in getting you to understand and empathize with why certain decisions are made, even if at the same time you are appalled and understand it as wrong through your own moral compass. At the same time, I think the film makes it pretty abundantly clear that having an insight into atomic power during a time that the Nazis were 100% trying to get there, and understanding it as an inevitability is quite a unique burden that none of us have had to live through. The scientists saw atomic energy as a fundamental piece of nature/the cosmos they were uncovering. That intersection between science and politics is the inherent tension that the film is all about. And there are so many ways those ideas can apply to the modern world beyond nuclear power.
I don't necessarily think the movie's grand statement is about Oppie being a coward either. To me it's more about how his naivete and self-importance were his undoing. I suppose you could include cowardice in there, that's up to the viewer. My view was he seemed to genuinely think that it would end all war, that he personally might be able keep the genie in the bottle. Or that he'd at least convinced himself of that. It's impossible to know for sure what he believed, which the film directly tells us. The whole thing about Oppenheimer is that he was a very ambiguous character. The film is more of an invitation to think about these moral paradoxes and character flaws and come to your own conclusions, rather than it is an attempt to reduce him to a single adjective.
More importantly though, where the film's sharpest political commentary comes from is rather from trying to judge the one man, it paints a very clear picture of the uneasy relationship between the government and science and how the government will listen to the science community when it serves their agenda, and cast them aside the moment it doesn't. That's where the ending really has its impact. It's about the realization that this ultimate destructive power is now at the mercy of the pettiness, vindictiveness, self-righteousness, smallness of men (IE Strauss) just viewing nuclear weapons as another tool in the endless Game of Thrones style jockeying for power rather than the world-ending threat they are. I found it to be a pretty damning and horrific view of American power. Everything that happens after Trinity really hammers that home for me. And I think any statements you want to read into the film have to be directly traced back to American Prometheus. It's a faithful adaptation that the author has wholeheartedly endorsed as having condensed the essence of the book.
As always, I think trying to read a film through a rigid political lens can be extremely reductive to art and tends cast aside all the layers of meaning and ambiguity that film, especially one this dense and complex, can invite you to engage with. Not entirely related, but I think this piece gives some context that I think is helpful in this discussion.
It's Okay for Art Like Oppenheimer to Make Us Uncomfortable