Neither one is good, though parts of 2 are better than all of 1.
Option 1 relies on dichotomizing the predicted probabilities using a threshold. Different thresholds give different values for all of these KPIs, and if you want to use a single threshold at all, you should choose it with a clear view to the decision being supported by the model. So the threshold is not a function of the model alone any more, but also of the subsequent decision. Therefore any KPIs that rely on this threshold will not depend only on the quality of the model. Accuracy and related KPIs like precision, recall etc. have major issues.
Parts of option 2 make sense, specifically $R^2$, which is essentially the MSE, which in turn is the Brier score. This is good. However, the MAE is not good, because optimizing on it will incentivize you towards heavily biased predictions: if your predicted probability for a given instance is larger (smaller) than 0.5, you will very probably reduce the MAE if you change this predicted probability to 1 (0). Optimizing the MAE is thus equivalent to optimizing accuracy - see above.
The accepted way to evaluate probabilistic predictions is to use a proper scoring rule. One such scoring rule is the Brier score, which is equivalent to $R^2$, which is why this is a least-bad option among the ones you suggest - but it makes more sense to explicitly work in terms of scoring rules, and to make use of the machinery and the theoretical results that have been developed around them.
However, note that if you are working in a specific decision context and understand the costs of various actions you could take in response to a probabilistic prediction, then it may make more sense to evaluate the entire model-decision workflow, because just optimizing the (say) Brier score will not necessarily give you the best decision (Assel et al., 2017).
