Should a WordPress plugin polyfill the global JS environment?

Does WordPress ship any polyfills of its own for the global environment?

No, as far as I remember WP core doesn’t ship with any polyfills.

What are best practices around handling/shipping polyfills in WordPress plugins?

The typical practice for JS in public WP extensions is to either:

  1. stick with core–provided scripts/environment;

  2. isolate your code and dependencies from impacting global state, by use of noConflict modes or otherwise.

If you have to deal with global state in public extension — be prepared for it to explode in most peculiar ways out there in the wild.