docs(phase-5): ship v2 docs to the dev version

Part of #224 — v2 docs rewrite (Diátaxis).

## Goal

v2 docs live on the `dev` version of the docs site; ready for the v2.0.0 tag.

## Tasks

- [ ] Merge dev-docs → dev; watch deploy_docs.yml deploy to the `dev` version
- [ ] Spot-check coder.github.io/balatrobot/dev/: nav, version selector, llms.txt, search
- [ ] On v2.0.0 tag: confirm `2.0.0` version deploy; after main bump, `latest` flips automatically

## Dependencies

- Blocked by: #225, #226, #227, #228, #229 (all phases)
- Blocks: nothing

## Done when

- [ ] v2 docs visible on the `dev` version
- [ ] Spot-check checklist verified

Read the deployment checklist and inspect deploy_docs.yml, which the issue names as the deployment workflow. After the dependent phases are complete and dev-docs is merged into dev, verify the deploy at coder.github.io/balatrobot/dev/ for navigation, the version selector, llms.txt, and search; done means the v2 docs are visible and the spot-checks pass.

Written by the indexing model from the issue text.