So, specifically, from which scientific fields will we lose all of this talent
Microbiology, neuroscience, solid physics, particle physics, robotics, ...
and to which countries will these people be moving?
Canada, England, France, Germany, Switzerland, primarily. Portugal has gone on a hiring spree, as has Poland and Australia. I haven't seen any postings from Spain or Italy, but maybe that's my field.
Further, in what ways will the NSF counterparts in these supposed other countries benefit R&D by foreign researchers?
I guess you don't understand how IP works. When a researcher works at an institution, the IP they generate is owned by that institution. The society where that institution is located typically is the big winner, as a result. Have you ever looked, for example, how much the US government gets in royalties from PCR?
No scientific talent will be "lost to overseas competitors".
The issue is that it isn't just DEI funding that's being cancelled. DEI is just the focus of the most bitter ire. There is a broad anti-science, anti-knowledge tone to the current administration, and I have many colleagues who have already left the US because of it. The number of available post-docs far outstrips the current number of open positions, and that talent is quickly leaving the US shores for greener pastures.