= Solution
The successful hard-margin fit proves that the transformed observations are separable. This creates <complete separation> in unpenalized <logistic regression>: scaling a separating coefficient vector continually raises the likelihood, so no finite maximum-likelihood estimate exists. The nearly singular observed information produces the enormous reported standard errors.
A ridge-penalized logistic regression, or equivalently a Bayesian logistic model with a proper Gaussian prior, gives finite, stable coefficients. Firth bias reduction is another standard remedy.
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