Welcome to the community. I am sorry you are dealing with this. I had a 9.5cm mucinous cystadenoma and was over-treated. My gyn removed all my organs even though the frozen section showed it was a mucinous cystadenoma which are benign tumors. Mucinous ovarian tumors that are cancerous are called mucinous carcinoma. I did not think cystadenomas could turn into cancer but I may be wrong on that.
If there really is a possibility that this cyst is malignant, you would want a gynecologic oncologist doing your surgery since they are the experts. If the frozen section shows that the cyst / tumor / mass is benign, you should not need to lose your ovary. But that also depends on the surgical skills of the surgeon. Some do not have good cystectomy (cyst removal) skills and even if they do, it is easier and maybe more profitable to remove the ovary.
Yes, removal of one ovary can impair fertility and even long-term health. There is no guarantee that the other ovary will take on the functions of the missing one. Plus if something happens to the remaining ovary, you are left without. After menopause, the ovaries switch to endocrine functions versus reproductive and continue producing hormones our whole lives. These hormones are critical for every aspect of health and well-being. I can attest to what happens after the ovaries are removed and it is not pretty!
Women who do not have a genetic risk for ovarian cancer have a very low lifetime risk of only 1.3%. You did not mention if you have a family history so thought I'd throw that out.
Best of luck and keep us posted on what you find out.