Hi, in my opinion, this is a Wordpress issue, not a Photoshop issue.
If you go to the media settings in wordpress, you can check the size of the images, if you upload an image, wordpress is going to scale the image according to the media settings, but for smartphones the idea is to use double the size since you have more resolutions on those devices. Depending of the Wordpress theme and the settings is how your image is going to looks like. My recomendations is to review your theme settings and support, maybe in this forum there are wordpress expert.
if you inspect the banner of your website, you can see how wordpress is handling the image
I hope you understand
My Best
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