fix(docs): rename apps/docs's start script to match its own convention

[os-project-manager]

Fixes#9086

The defect

pnpm docs:start has never worked. Both lines landed together in 159e29944 (2026-08-15): the root package.json delegate calls pnpm --filter @objectstack/docs start, but apps/docs/package.json declared site:start, not start.

Determination: the app's script name is the outlier, not the root delegate

Re-derived from scratch (not copied from the issue's provenance note):

• Root package.json's two sibling, already-working delegates map onto bare script names in apps/docs: docs:dev → dev, docs:build → build. That is the established, working convention.
• apps/docs/README.md (unrelated to this fix, pre-existing) documents the deployment step as:

  # From repository root
  pnpm docs:start
  # Or from apps/docs
  pnpm start
  

  i.e. the app's own docs already say the local command is pnpm start, not pnpm site:start.
• No other file in the repo references site:start — not .github/workflows/**, not apps/docs/vercel.json (which only sets a build command, not start), not scripts/**. Renaming it is safe.

So the root delegate was already correctly named; the bug is that apps/docs/package.json declared the wrong script name. Fix: rename site:start → start in apps/docs/package.json. The root package.json is unchanged.

site:lint is a separate, similarly-styled key but nothing in the repo delegates to it and it isn't broken, so it's left untouched — out of scope for this card.

Proof it was broken (on origin/main, HEAD 4e3a4c3c8, before this fix)

$ pnpm docs:start
> @objectstack/spec-monorepo@4.0.1 docs:start /home/user/objectstack-9086
> pnpm --filter @objectstack/docs start
ERR_PNPM_RECURSIVE_RUN_NO_SCRIPT None of the selected packages has a "start" script
ELIFECYCLE Command failed with exit code 1.
EXIT=1

Proof it works (on this branch, HEAD 5fd08318d)

Built the docs site (pnpm docs:build, exit 0, 1184 static pages generated), then:

$ PORT=48174 pnpm docs:start
> @objectstack/spec-monorepo@4.0.1 docs:start
> pnpm --filter @objectstack/docs start
> @objectstack/docs@4.2.1 start
> next start
▲ Next.js 16.2.12
- Local: http://localhost:48174
✓ Ready in 153ms

$ curl -sS -o /dev/null -w "HTTP_STATUS=%{http_code}\n" http://localhost:48174/
HTTP_STATUS=200

Confirmed the response body is the real docs homepage (<title>ObjectStack — A complete business system in 16k tokens</title>). Server stopped afterward (kill, then re-curled to confirm the port is closed — no server left running).

Note: next start prints ⚠ "next start" does not work with "output: standalone" configuration. Use "node .next/standalone/server.js" instead. — pre-existing, unrelated to this fix (Next.js config choice), and the server demonstrably does work (200 + real HTML) despite the warning, so not addressed here.

Verification

• node scripts/pm/dispatch-gates.mjs apps/docs/package.json at the final diff: 0 gate families name this path directly (101 discovered, 66 silent w.r.t. this path, 35 undetermined-by-source, 0 matched).
• pnpm check:nul-bytes (applies to any edit): green at HEAD 5fd08318d — check-nul-bytes: OK (scanned 5973 text file(s) ... no raw ASCII control bytes).
• pnpm docs:build succeeded (exit 0) at HEAD 5fd08318d.
• node -e "JSON.parse(...)" confirms apps/docs/package.json is valid JSON post-edit.

Changeset

Root-manifest/app-script rename only, publishes nothing → skip-changeset label applied; read back to confirm.

Out of scope

site:lint naming (same file, same site: prefix habit, but not currently broken/referenced anywhere) — not touched. Not filed as a separate finding: nothing invokes it incorrectly, so it doesn't corroborate #9089's "invocation actually fails" class.

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