Even if there is a pay gap, it's probably explained by women generally avoiding conflict, and men generally being more accepting of conflict. My useless anecdote is my wife will sign any contract without haggling, or go along with any authority figure. I haggle contracts and question authority. Women tend to seek to be liked / loved, and men tend to seek to be respected. It's in a businesses best interest to pay the lowest amount to satisfy an employee, and it's in the employees interest to demand the highest pay the employer is willing to pay.
The Jordan Peterson / Cathy Newman "discussion" is closest to summarizing my thoughts on the subject. In short, the reason for pay differences are many, and discrimination could be a factor, but it isn't the primary factor, or sole factor.
Regarding face to face vs online interactions, there might be some truth to that. The more barriers to picking up social cues there are, the easier it is to imagine the worst about someone. It's very easy to get angry at a car that cuts you off on the road, but then again, there is a lot separating the 2 people. I doubt many people would run around me as I'm approaching a line and jump in right in front of me.
Then again, there is always this: