My understanding is that a proof of reserves proves control of certain utxos. A lot of places also seem to be coupling this with some kind of liability proof.

This could probably be implemented any number of ways, but the important part is control over utxos. If they are using merkle trees, I imagine the merkle root would be useful for concisely expressing control, where leaves in the tree correspond to utxos under your control, which you can prove belong to the published root with very little other data.

There are a lot of resources listed on https://niccarter.info/proof-of-reserves/.