Hi Michelle,
You can try this snippet:
add_filter('generate_sticky_navigation_logo_output',function($output, $img_src, $image){
if( is_category(29) ){
$my_url = 'https://www.google.com';
$logo_src = 'https://cdn.reachingmyworld.com/wp-content/uploads/2022/06/18162522/Daily-Reach-Logo-For-Site.png';
$width = '150px';
$height = '150px';
return sprintf(
'<div class="sticky-navigation-logo">
<a href="%1$s" title="%2$s" rel="home">
<img src="%3$s" class="is-logo-image" alt="%2$s" width="%4$s" height="%5$s" />
</a>
</div>',
$my_url,
get_bloginfo( 'name', 'display' ),
$logo_src,
$width,
$height
);
}
return $output;
}, 10, 3);
Kindly replace 29
with you category ID