• Test.expect or any equivalent should be replaced with assert.strictEqual
• no random tests
• Node.prototype.push should also be implemented, if two different classes are used
• most likely a duplicate

No sample tests

Declaring BST as an object with a root that's a binary tree Node is a bad practice (and doesn't make much sense either), because it ignores the invariant that any branches of a BST is, obviously, still a BST; instead you only provide a weaker guaranteed that any branches of a BST is a binary tree. Also it makes the code of BST operations a bit more complicated because of this.

Declaring BST as an object with a root that's a binary tree Node is a bad practice (and doesn't make much sense either), because it ignores the invariant that any branches of a BST is, obviously, still a BST; instead you only provide a weaker guaranteed that any branches of a BST is a binary tree. Also it makes the code of BST operations a bit more complicated because of this.

The code and the Kata description are slightly out of sync

• BST versus BinarySearchTree

Error messages in Test Cases are incorrect.

Also, need random tests.

Again, move Node() and BST() to Preloaded?

Wouldn't it be cleaner to move the Node() and BST() definitions into the Preloaded section?

Documentation is in the Description already, and user isn't supposed to muck with it anyway.