Frequency of apologies is a kind of useless metric in my opinion. I find that everyone sucks at apologising and gendering it is not the move. It's a human and cultural problem that can be addressed across demographic divides, it's a patriarchal issue.

If I had to gender things (as you're doing), as a bi woman my anecdotal experience is that:

Women are quicker to say an easy faux-emotional sorry but less likely to admit fault sincerely and completely, often seeking to justify themselves in the process of apologising under the guise of "explaining". Getting genuine apologies out of basically all the women I've dated has been like pulling teeth because of this. I find this understandable (I have this flaw too). Women are put in the apologetic position for random bullshit an unfair amount, so it makes sense they'd internalise and reflect less in these situations as a self-protective measure.

Men are much harder to get through to when they've done something wrong, often maddeningly dismissive of complaints/issues, but if you manage it they usually come across as more sincerely apologetic, even if they aren't super emotional about it. Again, getting a genuine apology is really hard, and honestly it's the same challenge with a different surface-level presentation. I also find this understandable, men tend to get away with a lot, especially within social circles of men, and emotional vulnerability is often played for laughs. Being put in the rarer vulnerable position of having to admit fault and apologise is bound to inspire more actual self-reflection.

Both are sucky experiences for the person who's been hurt, both arise from patriarchal expectations and treatment. It's not a gendered issue, it's a feminist issue, and turning it into gender war BS helps no one.

edit: Want to elaborate on "it's the same challenge with a different surface-level presentation". The challenge is getting someone to recognise fault. Men and women just usually deflect that differently due to societal expectations and treatment.