The image you're using is in landscape orientation (wider than it is tall), at 1500x1000px.
That can fill the screen on desktop, but isn't going to fill the screen on mobile, without stretching it (even if someone did provide some custom coding to make it fill a larger space).
Most premium Shopify themes have an option to upload a secondary mobile image (right under where you uploaded the main/desktop image). It's best practice to use a secondary image for mobile, that's in 'portrait' orientation (longer than it is wide), rather than using the same image that you're using on desktops.
If your theme doesn't have this functionality built into, I'd recommend switching to a theme that does. You can add the 'demo' versions of themes to your store (before committing to purchasing them) to see what features/options are built into it.
With all that said, if you want to stick with your current theme (and if your current theme doesn't have the option to upload a secondary mobile image), then you could try playing around with the sizing of the image, to see if you can find a better size for working on both desktop & mobile.
Maybe try using an image that's perfectly square (ex. 1500x1500).
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