WP conditional site logo and header block

Considering you’ll use multisite and for adding logo you just need to go to individual site and enable option to add logo(will be available in the theme you are using).

Next step is to alter header.php from your theme and add following lines of code where you have the_custom_logo();
TO:

switch_to_blog( $blog_id );   //where `$blog_id` is current site id
the_custom_logo();
restore_current_blog();