How about we use a Hook element to place the image. So remove the header widget.
Create a new Hook Element:
https://docs.generatepress.com/article/hooks-element-overview/
Insert this PHP and HTML:
<?php
if ( !wp_is_mobile() ) {
?><a href="add_your_link_url"><img src="https://your-site/full_url_to_image.jpg"></a><?php
}
?>
Select the generate_after_header_content
hook
And set the Display Rules to Entire Site
.
The wp_is_mobile function ‘should’ detect its a mobile device and only output the HTML if it is !not a mobile device.
Once thats in there it will require a little CSS which i can help with.