Entity Browser Widget for Video Embed Media Entity
I could not find any way to implement an 'Add New Video' widget to an Entity Browser.

There is a solution using Inline Entity Form. https://www.drupal.org/project/inline_entity_form

With Inline Entity Form, you can have an entity creation option, or add existing entity option.  You can then use an Entity Browser for selecting existing entities, and leave the adding of new entities up to Inline Entity Form.

It's quite a clean User Interface / User Experience once implemented: