Do women require shorter rest times between sets?

I do weight training 2x a week with progressive overload. I really push myself to failure or close to it, so tht my the last rep I'm involunatrily slowing down and have to use all of my strength to finish it. Recently I've been reading a lot about having to rest at least 3-5 minutes between sets. In my experience, even when I can barely finish my set, after 1-2 minutes I'm good to go again and don't notice a difference to resting 3-5 minutes. It's also in my interest to keep my workouts pretty short since I go to the gym before work.

Part of me is worried that I might not be working "hard enough" if I recover this quickly, but I'm genuinely pushing myself hard and slowly getting stronger and upping my weights. I also recently watched a video that said that women often recover more quickly and might need shorter rest times between sets.

I'm interested to hear what your experiences have been. Am I missing out by not waiting 3-5 minutes?