Need help removing what looks like rust stains/dye stain from porcelain sink in bathtubs?

I have these gray/brown circular stains on my tub (photo attached). I think they might be rust stains, but I’m not 100% sure. I’ve already tried basic bathroom cleaner, and they won’t come off.
Does this look like rust, hard water, or something else? What’s the best cleaner to remove it without damaging the surface? Any recommendations for products or DIY methods would be appreciated!