I had the same issue and none of the above worked.
I selected the Facebook page from Facebook -> settings (upper-right corner) -> Messenger Platform (menu on the left) -> scroll down towards “Customer chat plugin” -> click the set up button -> copy the code at the end and place it into the header of your website:
1. Use a child theme
2. Use Google Tag Manager -> custom Html tag (this way you have control over the pages where the chatbot appears)
3. Use a plugin: Insert headers and footers
I hope this helps. It worked for: onegraphicstreet.com and darfil.ro
P.S.: don’t forget to delete your website’s cache (use a caching plugin) and then access it from incognito to see the changes.