How do I run a a priori sample size determination for non-parametric tests, like the Mann-Whitney U-test and the Kruskall-Wallis or other non-parametric tests that accord with the unpaired t-test (equal and unequal means) and the ANOVA? I searched in Rstudio and G*Power, but I couldn't find anything.

As the Mann-Whitney U has a power-efficiency of about 95% (with moderate to large N), relative to the independent t when all parametric assumptions are met, you could just increase the size of the N needed for t-test by about 5% to have a pretty good idea of requisite N. This would be a conservative approach to the matter; when not all parametric assumptions are satisfied, the MW-U may be more powerful than the t-test.

The same reasoning would apply to Kruskal-Wallis vs. one-way anova.

The Spearman correlation is simply a Pearson correlation run on ranked scores, rather than original score values. So, as long as you are thinking within the arena of, "how strongly do ranked scores fit a linear relationship," then the power analysis for Spearman rho would be exactly the same as for Pearson r.

A lot of data sets have outliers, so ranks and other procedures less influenced by outliers can be more powerful. For a great title to a paper see: Article ANOVA: A Paradigm for Low Power and Misleading Measures of E...