I see many people in this thread dislike umap for downstream tasms, but I don't see any good justification. I think umap is still regarded as one state of the art for top-down manifold learning among many academic researchers for deriving topologically correct embeddings with small local distortion.

For bottom-up manifold learning, I think the state of the art are based on local tangent space alignment. Here is one recent paper Low Distortion Laplacian Eigenmaps: https://www.jmlr.org/papers/v22/21-0131.html

In real life, the big issue for nonlinear dl is usually noise.