misc: rename typings/ to types/

[brendankenny]

Trivial rename. No functional changes to code. Part of #6202.

Somewhere around tsc 2.0 typings became passe and types was the way forward. Also, typings is really awkward to say.

Also updated some of our doc references into the type definition files. Two of them still point to typings as that's the only thing currently on master, but the references are way better now (e.g. Audit results have docs now, before, after).