There are non-parametric alternatives for 2-way factorial models.

Most af these are aligned ranks tests.

See: the ARTool: https://depts.washington.edu/acelab/proj/art/index.html

and or The nparLD R package

These assumptions need to be tested before you can run a repeated measures ANOVA. Fortunately, the repeated measures ANOVA is fairly "robust" to violations of normality. "Robust", in this case, means that the assumption can be violated (a little) and still provide valid results.

https://statistics.laerd.com/spss-tutorials/one-way-anova-repeated-measures-using-spss-statistics.php

For checking the assumptions, see, e.g.:

https://www.datanovia.com/en/lessons/anova-in-r/#check-assumptions-1

You should check the normality of the residuals.