EU is first, with foolishly predictive tech regulation before it emerges. Like e.g. the requirement for AI to explain itself. GPT can surely explain to you very elaborately how they came to the wrong medical conclusion
But what you say is actually accurate, the globalized world (excepting russia) has settled to these roles for these 3 players. EU is more of a legacy player without an army (or strong production base) that still "upholds ideals" and sells this image for worldwide PR. But you see where this ends up, countries bribing EU politicians to improve their world PR by association.
China: I'll bring the hardware!
US: I'll bring the software!
EU: I'll bring the lawyers!