Is there a way to enable Basic Auth for only one specific type of node?
Probably there is no one here, that has tried the method you've described. I would start with a custom entity, use the basic auth or create a new authentication provider and apply this for the entity route. You can do this with drupal console within a minute.

And you don't need contrib code to configure access for the custom entity, because here you can do what you want in core. I wouldn't use an Access plugin from contrib, until there is a stable release.