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As the question entails, I would like to know as a rule of thumb, an upper limit on the number of features I could have for a data set with 1,000,000 rows/observations, before hitting the curse of dimensionality. If not a million observations, an answer with a rough estimate for the number of features for a data set with a specified size would be great too.

Thanks

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The curse of dimensionality means that your intuition fails at a certain number of features. See Average Distance of Random Points in a Unit Hypercube for some examples. It does not matter how many points you have.

For example, at around 100 dimensions every two points randomly sampled points are really close.

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