OC does run in my family on my mothers side. They call it the family curse. Every woman on her side without a complete hysterectomy by about my age or before has gotten or died of some form of lady cancer. Be it cervical or ovarian. And just recently I lost 2 family member on my dads side an aunt and a uncle less than 6 months apart to lung cancer. We didn't even know they had it till they passed. So needless to say I've lost a bit of sleep over this. My mom and grandma had complete hysterectomies at younger than my age or near my age. My great aunt Katy had cervical cancer and is in remission and lost her bits and pieces. As well as a double mastectomy. Lost all my great aunts to different female cancers.
I recall your other post and responded to it but I do not recall if you said you have a family history of ovarian cancer. If you do, then that is more concerning. If you do not, then hopefully, you would fit the statistics for this cyst being benign since the average woman's lifetime risk of OC is less than 2% (1.4% per U.S. government statistics).
You said instead of being referred to an ob/gyn, you are being referred to a surgeon. Ob/gyn's are surgeons (at least in the U.S.) so maybe they referred you to a gynecologic oncologist which would be good since there is a chance this could be cancer. But the size itself (12cm) warrants surgery, cancer suspicion or not.
You will want to question the surgeon's plans for both scenarios, benign and cancerous. If the cyst is benign (per the frozen section done while you are under anesthesia), you may want to make sure only the cyst is removed (cystectomy) since the ovaries are important for overall health as well as optimal fertility. Of course, this all has to be weighed against your OC risk which you may or may not have inherited (if there is even OC in your family). Not all surgeons have good cystectomy skills so you could still lose your ovary for a benign cyst.
I was grossly over-treated (both ovaries, uterus, and tubes removed) for a benign cyst even though I had no family history of OC. I was a lot older than you (49) but it has affected my life in many ways. I wish I had done a better job of advocating for myself including revising the surgical consent form.
I hope this helps you get appropriate treatment. Please keep us posted on how this progresses. And don't hesitate to ask questions, research, seek other opinions, etc.