How to visualize the results of the statistical tests?

Which p-values for tests with > 2 groups?

On graphs that show the results of ANOVA or Kruskal Wallis you show the p-values of the post hoc tests like Tukey, Dunnett or Dunn because you want to show the pairwise comparisons.

In the text you mention all the p-values, both those of the ANOVA or Kruskal Wallis test and those of the relevant post hoc tests.