There is no such clean interpretation for UMAP. It's non-linear, which is nice because unlike PCA it will reveal structure beyond linear relationships. Unfortunately by doing this you lose the connections to linear algebra which is the basis for inferential statistics. These non-linear methods are just nice visualization techniques to justify further exploration with other tests, but you should not spend too much time reading into them (though it can be fun, it is ultimately a waste of time).
There probably are nice interpretations of UMAP, but it is not within linear algebra and requires a lot more advanced math as UMAP is based on Reimannian geometry. https://arxiv.org/abs/1802.03426
UMAP may have predictive value in some circumstances in ML, but building a predictive model is not the same as making inferences.
What is the difference between prediction and inference?