> A question for Mathematica-folk: does Mathematica have support for direct manipulation like Toby Schachman's works?[] I find direct manipulation more pleasant than typing characters.

Locator comes to mind:

https://reference.wolfram.com/language/ref/Locator.html

https://youtu.be/6wOLBVFdek8?t=11s

And more generally Manipulate which makes it easy to whip together a let-me-explore-how-this-depends-on-that type of widget.