Immigration will play a major role to disrupt the picture you painted. In addition, the transition of economic leadership would not be a smooth one in the best of scenarios. I believe there is even a chance of a world war which would be catastrophic for the human race and life on earth.
First immigration: When China becomes the world's leading power there will be a lot who will want to emigrate there irrespective of the level of racism present. Economics trumps racism and bigotry. For example, in the US, we've seen immigrating women being forcefully sterilized https://www.bbc.com/news/world-us-canada-54160638 and children separated from parents and put in cages https://www.hrw.org/news/2019/07/11/written-testimony-kids-cages-inhumane-treatment-border and yet, still they come. And the reverse is true. When economies collapse there is net outward immigration. So, net immigration may stop in the US and possibly reverse depending on the economic climate.
Second is the economic transition: The most important factor in the economic transition of power is on the de-facto world currency. Currently, US dollar reserves in foreign countries is around 15 trillion dollars (my estimate, I added the reserves of the top 80 countries in US dollar reserves). The US also benefits from every international transaction which is mostly denominated in dollars. The SWIFT system is how the US imposes devastating unilateral sanctions and benefits from those transactions. Today, services is 80% of the US economy, which in my opinion, primarily relies on the dominance of the dollar. What happens if the Chinese currency (Yuan or E-Renminbi) becomes the world currency? Most of the 15 trillion dollars in reserves will be flushed back to the US! What do you think will be the effect on dollar inflation and on currency exchanges? Eventually, I believe the US economy will stabilize, but it will have a catastrophic few years up to probably a decade or so and will never return anywhere near its dominance. The reverse will happen to China! Countries will want to exchange dollar reserves for Yuan reserves and every transaction in the world will benefit China ...
That 'browning' you talked about will flow into China and away from the US which will become economically devastated for at least a decade or so.
How will China react to becoming the new leading power? How will it treat its immigrants? Those are other questions, but the human flow will follow the economic one and China will accept what it needs because it has shown every indication of being pragmatic in everything it does.
All this assumes there is no world war and humanity or at least civilization, as we know it, survives the transition.
