AUC-ROC to evaluate threshold-independent separability is correct because it measures how well a model ranks positive examples above negative ones across every possible decision threshold.

AUC-ROC to evaluate threshold-independent separability aggregates true positive rate and false positive rate over all thresholds and the area under the ROC curve quantifies class separability so a higher area indicates the model better distinguishes spam from legitimate messages independent of any chosen cutoff.

Confusion matrix at a chosen score cutoff only reports performance at a single threshold and it cannot show how the model behaves as you change the decision cutoff so it is not suitable for threshold-agnostic comparison.

F1 score computed at a single operating point gives a balanced measure of precision and recall but only at one operating point so it does not reflect performance across all thresholds.

Average precision on the precision and recall curve summarizes ranking quality in the precision recall space and it is useful for imbalanced datasets but it emphasizes precision recall trade offs rather than ROC separability which is the specific concern when comparing models across every possible cutoff.

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