This is an issue with many facets, but I remember study results coming out a few years ago: https://www.nytimes.com/2016/03/20/upshot/as-women-take-over-a-male-dominated-field-the-pay-drops.html

Your example of a plumber is interesting and I want to pick on it a little. I'm the US, where the majority of skilled tradepersons are non-union, so the employer sets the wage. In theory, women non-union plumbers could make less overall than ones who are men. I don't know if it's ever been studied.

I joined a union, and my wages are dictated by my contract, so I make as much as my majority male co-workers, who are highly paid. This is good for me, and I encourage women to enter skilled trades. I do wonder what will happen to wages as we come closer to parity in numbers of men and women in the trades.

I know unions aren't perfect, but I believe in worker representation. But if you look at public school teachers, who flipped to being majority female years ago, in a "caretaking" profession like the Times article refers to, it doesn't matter if you have a contract if you're coming into a profession in which wages tanked years ago.

There is also the motherhood penalty, which is real. https://nwlc.org/press-releases/mothers-lose-16000-annually-to-the-wage-gap-nwlc-analysis-shows/#:~:text=Mothers%20Lose%20%2416%2C000%20Annually%20to%20the%20Wage%20Gap%2C%20NWLC%20Analysis%20Shows,-Posted%20on%20May&text=Mothers%20typically%20are%20paid%20only,NWLC)%20analysis%20of%20Census%20data.

I think you're correct when you notice these issues are systemic. It's beyond lazy for men to call the wage gap false when casual observation shows us otherwise, backed up by reputable studies.