The US (which I'm a part of) has no authority over the CMA, or the EU, and should mind it's own borders and business.
If the United Kingdom government intends to impose multi-billion-dollar (or -pound; doesn’t matter) fines on two
American corporations, demand restrictions on who can be directors, officers, or executives of those corporations, and/or demand changes to the ways those corporations design their products, they will find that American-government cooperation is crucial for any hope of enforcing those restrictions, actually.
The consequences that are within the unilateral power of His Majesty’s government—to wit, restricted access to a populace that provides
maybe 5% of global spending on tech products and services—are pretty meager, and they come with obvious political risks. UK voters might be rather unhappy if, thanks to a fight their government has picked, it suddenly becomes much harder for them to buy an iPhone, use Google search, or watch “Severance.” And they would be capable of taking their frustrations out on the elected officials who make those restrictions possible.
The same considerations apply to politicians in the EU, though the potential monetary losses to the tech companies are a little larger. It’s interesting to wonder who would crack first if a few major companies decided to “go on strike” and refuse to do (official) business in small markets whose leaders think they have the power to coerce the companies to make major, ruinous changes in the ways they design their products.
It’s not at all clear that these governments are nearly as powerful as they think they are.