test-hygiene: restore the windows-flake-soak workflow test and type-check script/qa

Restore the dedicated soak workflow test deleted in b95b0789 and align it
with the current windows-flake-soak.yml allowlist. Fix the six TS2322
ManagedRunner assignments in script/qa/omp-item2-eval.ts and
script/qa/omp-item2-invalid.ts, and include script/qa under the CI
typecheck:script project so those files cannot rot silently.

Fixes #8361