Eliminate special-casing from test CI workflows. (#9562)

The previous approach was relying on `_test.yml` taking an input
parameter, and then doing almost completely orthogonal things for each
parameter value. I've separated out each of those test situations as its
own job or workflow file, which eliminated all the special-casing and,
in my opinion, improved maintainability by making it much more obvious
what code runs when.