Hi, you need a MANOVA instead of an ANOVA if you have more than 1 outcome variables. Even if you are not interested in the relationship between the two outcomes, a MANOVA can be more sensitive / can have more power compared to 2 separate ANOVAs. But especially if you have only two outcomes and you say you are not interested in the relationship between them, I think two ANOVAs are OK for your purposes.

"...each of which received a different treatment over 4 sessions..."

Keep in mind: As soon as you have repeated measurements of the same participants, you have to use a mixed ANOVA, since this is not anylonger an independent design.

You need non-parametric ANOVAS only if parametric assumptions (such as normality of the outcome, homogeneity of variances...) are not met. If they are met, you should use parametric tests since they often have more power compared to non-parametric ones.