how to set custom logo (not the site identity icon)

i’m developing a classic theme and somehow i have a logo that’s not the site identity, it is placed in header and works great locally but when i applys the theme online i cant show that logo altough it’s on media library
but i noticed something locally that the image of logo has a detail says: used as: logo

the site icon has another photo with another property

// the function that i use to retrive the logo to put it in header
<?php if (!function_exists('my_logo')) {
  function my_logo() {
    $custom_logo_id = get_theme_mod('custom_logo');
    $logo = wp_get_attachment_image_src($custom_logo_id, 'full');
    echo esc_url($logo[0]);
  }
}

BUT .. online i can only set site icon but cant set that logo and it doesn’t show up, so i’m asking how to set it