Test/update API module for new Parser code version

The PHP parser we are using has a new stable branch, 4.x, which can be found here:
https://github.com/nikic/PHP-Parser/releases

I suspect that the API module will not fully work with this version without some modifications. And this issue may be due to that user having 4.x (not sure yet): #2961876: Error Running Drush cron after Hitting Reparse →

Anyway, in this issue here, we should
(a) Test the API module with the new Parser code. Note: it requires PHP 7, and api.drupal.org doesn't run PHP 7 yet, so this issue is postponed until that is a possibility.

(b) Fix anything that doesn't work

(c) Update the composer.json file to require that new version, once it's working

See also #2935714: Some comments inside switch statements are duplicated in code output → , which was fixed by a new parser release (3.1.5 but it is also fixed in 4.x)