The effect size for robust RM ANOVA is not available because it is not yet implemented in WRS2 package, which statsExpressions relies on.
You are right, the degrees of freedom for ggbetweenstats and ggwithinstats are different because they run different kinds of tests; the former ANOVA, while the latter a repeated measures ANOVA.
Here is a good introductory tutorial on dfs are computed for RM ANOVA:
https://statistics.laerd.com/statistical-guides/repeated-measures-anova-statistical-guide-2.php