I recently found out the hormonal patch is plastic and it got me wondering if that makes it water impermeable. I have always assumed it is just like the usual plaster used to cover wounds.
Yes, or at least waterproof enough to bath and swim while wearing it.
According to the Association of Reproductive Health Professionals:
You can wear the patch while bathing, showering, swimming, and exercising
And the NHS:
You can wear the patch in the bath, in the swimming pool and while playing sports
And according to the review Transdermal ethinylestradiol/norelgestromin: a review of its use in hormonal contraception.
During three efficacy studies in which more than 70 000 patches were used (7-day duration of application), 1.8% were replaced because of complete detachment and 2.9% for partial detachment. Neither living in a humid climate nor physical activity, including exercise, heat, humidity, and water immersion, seemed to affect patch adhesion
If the patch detaches, it needs to be replaced, but water immersion such as bathing and swimming does not appear to significantly increase the risk of it happening. Water immersion also doesn't reduce the hormone uptake of the patient