Looking at your source, all these states have increased the percentage of college-educated adults from 2006, which doesn't really indicate a brain drain.

Looking at two states each with one-year increases (Maine, West Virginia) and decreases (California, Louisiana), the one-year decrease doesn't seem to be particularly related to any longer-term trend.

2006 2020 2021

California 29 36.9 36.2

Louisiana 20.3 27.2 26.4

Maine 25.5 33.5 36

West Virginia 16.5 23.1 24.1