What the research shows, and what it does not settle
Two findings, and the second one is honest about its own limits.
What the research says
Cassady JC, Johnson RE (2002). Cognitive test anxiety and academic performance. Contemporary Educational Psychology, 27(2), 270 to 295 doi
Test anxiety splits into two parts that behave differently. The physical part is the racing heart and the shaking. The thinking part is the worry and the self monitoring during the exam. It was the thinking part that carried the relationship with worse performance, which is why a student can feel physically settled enough and still lose marks.
von der Embse N, Jester D, Roy D, Post J (2018). Test anxiety effects, predictors, and correlates: a 30-year meta-analytic review. Journal of Affective Disorders, 227, 483 to 493 doi
Thirty years of studies pooled. Test anxiety and exam performance are consistently linked in the unwanted direction. The authors flag that the measures differ a great deal between studies and that most of the designs are correlational, so this literature on its own does not settle which is causing which.