AUC-ROC interpretation for a binary classifier

I have this confusión matrix results:

True Negatives : 725
False Positives : 74
False Negatives : 62
True Positives : 139

precision    recall  f1-score   support

False       0.92      0.91      0.91       799
True       0.65      0.69      0.67       201

accuracy                           0.86      1000
macro avg       0.79      0.80      0.79      1000
weighted avg       0.87      0.86      0.87      1000


And plotting the ROC curve I got this:

AUC ROC=1.000

MCC (Matthews correlation coefficient) = 0.6412

Is clear that according to the literature, the classifier is doing perfect, but I'm skeptical considering that I got the same image (with a different confusion matrix) with a threshold of 0.5 and even with 0.2.

I'm not sure if I'm doing well and if AUC ROC is the more appropriated to measure my classifier. Considering this is my first time dealing with AUC ROC curves, what else should I do to resolve my concerns?