I want to compare within distances between groups after beta diversity analysis. For example, there are two groups - A and B. I want to show that samples in group A have a more similar microbial composition than that of samples in group B. I could extract distance data of "A and A" and "B and B" from PERMANOVA results. Group B shows higher values than that of group A.
In this case, are there any specific methods available in QIIME2 to compare within-group distances between different groups of samples? Can I just use a general statistical test using these values like the Mann-Whitney test?

I want to know the first one. So I want to show group A shares more features between samples than group B. Looks like 'permdisp' is a good option in my case, right?

(It's a subtle difference and simple English is ambiguous )

At the risk of making this more confusing, here's another way to say it:

The binary Jaccard distance reports the fraction of features that are found in only one sample.

So if all features are shared, then binary Jaccard = 0.0
If 80% of features are shared, then binary Jaccard = 0.2

The goal is to show that:
the mean binary Jaccard distance between samples within group A
is not equal to
the mean binary Jaccard distance between samples within group B