I think a more mundane explanation, which I personally subscribe to, is that Europeans have different priorities than Americans. They don’t want the same trade-offs, and they’re willing to make certain business models economically unviable if they believe those models are harmful or in bad taste. US companies are disproportionately affected because they don't share those values. First amendment, etc.
From the outside, this can create the impression of "hidden motives": the stated reasons sound unconvincing, the effects fall heavily on US companies, and so people infer that the EU is targeting Americans. But really, I think we're just different. If US laws disproportionately burdened EU citizens, I’d expect Europeans to be equally upset. It's only natural. I'm sure few people in Europe would be thrilled to find out that GDPR doesn't apply to ChatGPT because they got involved in some copyright lawsuit in New York.
That said, there's always a mix of motivations. I'm personally not a fan of other EU initiatives, like the one on encryption, but I think GDPR and DSA mostly mirror what the average João wants. I'm not sure most people care that much about the geopolitics.
It doesn't though, it applies those laws if the entity in question happen to also be slurping up a bunch of user data and selling/using it for various purpose, something which requires intent and active work to do.
If they instead didn't do those things, these laws wouldn't apply to them in the first place. Random American HN users just having a website public on the internet without perverse tracking has nothing to worry about, and does not have to care about GDPR, EU rules or much else.
That's information war. We should probably ban on sight but as we are free countries, we put in place a regulatory framework and let the courts do their work.
You don't want balkanization of the internet? Tell your government to stop using it as a weapon.