This is something you’ll find different answers to across the online forums. So take my answer here with a grain of salt, as a non-statistician.
The answer depends on what your question is and how your model is set up. Given that these are time-point data, I assume you were interested in the effect of Groups across time on microbiome alpha diversity measures.
Is your formula set up to detect interactions? i.e. diversity
~ time*groups? If so, what are the significant effects? If you see a significant effect of
time*group, I don’t really see a benefit of doing post-hoc tests at each time point. Your answer is very clear, that microbiome changes exist within each group and these changes are different across time. If you see an effect of time but not groups, then again I don’t see a point in your post-hoc test because you determine groups were not different, so you don’t care about the time effect by itself. If you see a sig effect of group but not time, then it might be worth looking at each time-point to see perhaps at what specific time point things were different. In that case you should adjust your p values in your post-hoc tests specific at each time point. At least this is what I do.
If your formula does not have an interaction term, then you should only do a post-hoc test if there was a significant effect of Group. Again your post-hoc test would adjust for p values at each time-point.
Again, reiterating that I am not a statistician, so you’ll want to check this with someone trained as so.