Partially rewrite docs linter

1. I want to set the stage to deal with MithrilJS#2898 properly.
2. `request` was deprecated years ago. Decided that it's better to just
   move to native Node.js APIs in its place.

I also decided to go a few steps further:
- Task queues to control concurrency
- Reimplemented the lint recursion manually
- Drop the cache to simplify everything
- Upgrade to a more modern language version

.gitignore

@@ -5,7 +5,6 @@
 /.vscode
 /.DS_Store
 /.eslintcache
-/.lint-docs-cache
 
 # These are artifacts from various scripts
 /dist