Circadian rhythm data is becoming more and more common (gut-brain axis, metabolic disease, etc.), so having features that support that kind of dataset would be great. It has all of the same considerations as longitudinal data, but with the added problem that there is know fluctuations/volatility within the day (more or less match cosine waves).
For example, I love LME for longitudinal datasets, but for circadian datasets I would need a non-linear mixed effect model.
The main tool used by the field to determine cyclic patterns right now is MetaCycle (R) mainly using the JTK_CYCLE method. Validated on yeast transcriptomics and not made specifically with microbiome data in mind.
There are also a few methods that determine rhythmic patterns DODR, LimoRhyde (R), and CircaCompare (new, 2020) but all methods were based on using yeast transcriptomics data, which may not be appropriate for sparse datasets such as 16S. (I am unsure about metagenomics as I have minimal experience processing that type of data, but presumably that as well.) They are not widely used by the field as of yet, but that appears to be starting to change.