Do you imagine China may one day claim they own all the rights to all the objects labeled with “Made in China” on them? Could Anthropic possibly do this?

I would say the answer is "obviously not," to the degree that it's hard totake your question in good faith.

The China-made goods have been sold. Ownership transfers at sale. It would be ludicrous for some Chinese agency to say, "Well, we made it, so even though you bought it from us, it's actually still ours. Surprise!"