[JS] Add ability to run tests in headless browsers

Now that we have a compatibility check that modifies behavior based on the features in a supported browser, we should really be running our tests in various browsers to exercise the various cases.

For example right now we don't actually run tests on the non-BigNum code.

**Reporter**: [Brian Hulette](https://issues.apache.org/jira/browse/ARROW-5740) / @TheNeuralBit

_{**Note**: *This issue was originally created as [ARROW-5740](https://issues.apache.org/jira/browse/ARROW-5740). Please see the [migration documentation](https://github.com/apache/arrow/issues/14542) for further details.*}