Finish transition to Lerna by clarifying release management steps, updating release script

Doing some more lerna-changelog testing by giving this one a breaking label. Also some tweaks below.

Changes

yarn run publish -> yarn run release to avoid a conflict with the publish script
Added version script to update the changelog immediately after package.json is updated.
Improved release management docs

[ ] PR has an informative and human-readable title
[ ] Changes are limited to a single goal (no scope creep)
[ ] Code can be automatically merged (no conflicts)
[ ] Code follows the standards laid out in the development playbook
[ ] Passes all existing automated tests
[ ] Any change in functionality is tested
[ ] New functions are documented (with a description, list of inputs, and expected output)
[ ] Placeholder code is flagged / future todos are captured in comments
[ ] Visually tested in supported browsers and devices (see checklist below :point_down:)
[ ] Project documentation has been updated (including the "Unreleased" section of the CHANGELOG)
[ ] Reviewers requested with the Reviewers tool :arrow_right: