How to prepend a header section to all pages related to my WordPress Plugin

it didn’t work for you because hook admin_head is designed to add <link> tags inside <head> section. So even if you will render something there it won’t be visible, because it is outside <body>.

If you want to render something after admin head bar, you should use wp_after_admin_bar_render hook:

To determine if you are on a page where your tab should be visible, you can use the function get_current_screen():

Inside this link, you have an array with description what code you should use for certain pages.

Probably you will need additionally to check post type in edition page, but you can do this using the same function like that:

if ( 'your-custom-post-type' !== $screen->post_type ) { 
  //this is not our custom post, so let's exit

Hope this will help.