I don't think the trend toward treating men's and women's teams the same will impact college sports much. First, I'll note that tennis and soccer are the only two sports where the revenue generated by the women rivals that of the men. In other sports the gap is far to big to reconcile. And looking at the details, there is no parity of compensation in soccer broadly (there is in tennis because the women bring in similar revenue). The only parity in soccer is the compensation paid to the US men's and women's national teams, because US Soccer decided to do that. Given the wild popularity of the women's team, and given that the goal of US Soccer isn't to generate revenue, and given US politics, that made sense to US Soccer to do. However, I don't think this has any bearing on what will happen to college sports or is indicative of what is happening in pro soccer or pro sports generally.
For instance, in 2018, the prize pool for the Men’s World Cup was $400 million, whereas for the 2019 Women’s World Cup, it was $30 million. That won't change because it is indicative of how much actual money each tournament generates. There is no conceivable way that, just to be nice, all the men will agree to donate half of their earnings to the women's teams. The same is true for club salaries of professional players. In edit: the prize money for women in '23 was 150M and for men in 26 is projected to be 900M. So the gap is closing, but still overall pegged to popularity and revenue generation.
In addition, for sports where there aren't women's and men's teams, if DOE goes the enforcing parity road, would they have separate rules? How would field hockey compensation be handled relative to football? The women's basketball team gets rich, because the men's team is forced to split evenly with the women, but field hockey get's nothing because there is no parallel? It doesn't make sense.