docs: split TESTING.md into focused per-type docs (#1192)

* docs: split TESTING.md into per-type docs with manual testing requirement

Break the monolithic TESTING.md into focused files under docs/testing/
(unit, integration, TUI, browser, e2e, manual) and add a requirement
that every change must be manually tested before submitting.

* fix: address review comments on testing docs

- e2e-tests.md: use correct `npm run test:e2e` command, add AWS creds prerequisite
- manual-testing.md: fix tarball glob to `aws-agentcore-*.tgz`

* style: fix prettier formatting in testing docs

Author: jesseturner21