I do not see endorsement of misogyny in the Bible. In fact I see very little of it. I do however see that Men naturally have sinfully hurt one other/women. I do not however think that is endorsed.
God saved many women throughout a misogynistic society in the OT
Think Rahab
Joshua 6:17 , Esther , Hagar, Naomi/Ruth, he looked favorable on those oppressed think Leah, and Hannah. He even had at one point a woman lead, Deborah.
Now in the NT I see examples of what roles men and women are supposed to act out in the Church. It is because we are equal in position ,inheritance , and value but separate in role. We are not men, and men are not us.
To be a woman is a joy, we are instructed how to conduct our lives as one.
Being a man is amazing, they are instructed how to conduct their lives as one.
It looks super different, but one things for sure: we are both called to sacrifice, submit, love one another, forgive, extend grace.
I would actually argue that it could be seen as more difficult for men as they have a higher authority(specifically limited to husbands and church leaders/elders) as they are held accountable for the teaching of others.
But here's some scripture on how men are supposed to live:
1 Peter 3:7
Ephesians 5:23
Ephesians 5:33
1 Timothy 3:2
1 Peter 3:6
Titus 2:2
Titus 2:5
Here's some scripture on how women are supposed to live:
Ephesians 5:22–33
1 Peter 3:1–5
1 Timothy 2:12
Titus 2:3
Titus 2:5
Scripture about our union:
Genesis 2:18
Genesis 2:24
Proverbs 18:22
Mark 10:6-12
1 Corinthians 7:1–16
From these and some I haven't listed we see that men have a high standard to live by, and women
Men are leaders in the church, women not as much with exception.
Men have authority over woman in marriage and as a church Elder/Pastor. But God has authority over all.
Men are called to sacrifice, love, consider and understand and be kind to their wives. And we are all called to be loving, sacrificial and helpful. Patient and self disciplined in general.
Woman are called to be obedient to church leaders, as are men as well. But woman is not permitted to teach in authority over a man, and are to be submissive and obedient to their husbands. We are to be loving, respectful, and kind. Not fearful or controlling.
The ideal role for woman is as a wife raising a family, I believe but some may argue. Of course this my only be a aspect of ones life.
This is long and i'm sorry! Scripture just has a lot to say here. I love womanhood and manhood and I believe it has great value if we live it out right. God has made things to be this way.