Wordsmith integration pages and fix various issues

This wordsmiths the integration pages and also fixes various issues like unclosed HTML tags, missing examples, spelling, grammar,  headings, etc.

**Note:** This does not fix the missing sections on how to add locale data to the pages — that'll be in another PR.
This aligns with what's in their repo, and for our examples, you'd need `dust-full.js`. It also aligns with our packages.