What other tests have you had? Any nutritional blood panels?
I had everything you've listed - periods vanished for months at a time, I had cysts on my ovaries (identical on each side which one HCP found a fascinating coincidence), depression, odd appetite and weight gain in ways I don't tend to (I normally gain more in thighs/hips/upper arms, but I was suddenly gaining in the waist and face).
I was misdiagnosed with premature ovarian insufficiency/early menopause for 5 years based on my symptoms. I only found out after 5 years and taking the NICE guidelines on menopause practically begging for treatment as I felt so low and like I wa falling apart as more menopausal symptoms appeared that a GP dug through my records to find out none of the diagnostic tests (like the previously mentioned LSH and FSH levels) supported that diagnosis, it was just the easiest with my symptoms.
It ended up being multiple nutritional deficiencies, a couple very severe, that needed on-going management to bring me back out of. I'm going to have to carefully manage my diet and supplement a few things for the rest of my life as I seem to struggle to absorb (or in the case of Vit D, make from sunlight).
Bodies are weird, that group of symptoms could be many things - including PCOS, but I think more information would probably help you understand it better whichever it is. At least exploring options like inositol (usually paired with folic acid) which has some early but interesting results in helping that may be better than metformin if you don't have current insulin issues.