How to theme video_embed_field per node type
Twig naming pattern for the field per content type is

field--field-name--content-type.html.twig


Read more on Twig naming convention here.



update

Media entity seems to be following custom template suggestions, that unfortunately are not documented anywhere. See function media_entity_theme_suggestions_media() here for template suggestions patterns. It does not include per content type template suggestion, but you can try overriding it in a custom module.