In the early days, on the surface, it would all be peace and love. Women would find more peaceful ways of resolving conflict. The men would be protected by their partners so they wouldn't be taken to the Sperm farms
However a group of women with power would be carefully planning what happens next
All available men would be rounded up, screened and allocated positions. Those with good sperm counts would be kept as brood mares. They would be expected to make regular contributions of sperm which would be frozen for future use. The richest and most powerful may also use them for sex.
A few night be highly revered for their specific skills bit within a few generations, as they got older and died and other women took their spot less so.
Baby boys born would be given to the most powerful families to raise, before being sent to the Sperm farms. This would be considered a noble action and live bit there would be little choice really. Of course birth mothers would try to hide them and these women would face death or imprisonment for going against the Chief Matriarch. Some women would go so far as to castrate their own sons in the hope of protecting them. This would be punishable by death for both.
Women wanting babies would have to be screened for congenital illnesses, mental health issues etc and there would be a cost. Babies would be limited to 2 girls. If you have a boy, because he'd be taken from you, you could have another sample of sperm free.
More women would form lesbian relationships.
Being trans Would be outlawed as it would be seen to mock the Matroarchy