What a gorgeous ottoman.

I think I would leave the legs, but would you like to post a photo of it with your other furniture?

I would stain darker, I think it would really make the green stand out

The description says it's larch wood, probably from China, I expect. You could always paint the legs in a glossy black if staining them doesn't give you the effect you're looking for.

Looking at the picture on my phone now with better colour and I definitely think you should darken them! They don't have to be as dark as the furniture legs, you could darken them a bit and see if you like the tone. If not it you still have the option of going darker.