How to detect that the save_post hook is calling the callback associated to the current edit post page only

Any function hooked to the save_post hook will run whenever you save a post. That is expected behaviour.

You should use the hook save_post_{$post->post_type} to specify to which post type that callback is asociated. That way, it will only be called when saving a post of type {$post->post_type}

See the hook documentation