What’s the Idiomatic Vanilla JavaScript way to bind data and UI in a web browser?

The whole thing boils down to creating objects (the constructor is built-in) and using functions on objects. Functions are objects, too. In fact, everything except primitive values are objects.

IMHO knowledge of C++, Python, or pretty much everything that's not a lisp variant, doesn't translate well to JavaScript.

There's such a nice language with its own silly warts, readily available to pretty much anyone with a computer regardless of form factor, being misunderstood by the vast majority of programmers.

Web components, invoker commands API, etc.

What are you really asking? You use data to populate content or inform your logic.

With webcomponent each tag is a component instance that can hold data and there are hooks for attributes change