2 problems : import component & send messaging

Good morning, I have 2 problems. The first: I need to have child components in the content script. Now if I create the child in the contents folder and import it in the classic Vue way, then I find this component on its own in the injection page and not as a child of my script (img 1 & 2 ) . however, if I insert the child into another folder, it is not displayed on the page at all (img 3) The second: I need to send data as a message from content to the popup, if possible directly, otherwise via BG. I've tried everything in the documentation but it doesn't work for me