docs: correct the dependency-classification claims

Copilot review round 2, four findings, all factual errors in the docs added by
the previous commit:

- `yaml` is in the root `dependencies`, not `devDependencies`, and its only
  importer is `test-servers/src/load-config.ts` — not `core/` or the root
  tooling, as the `vitest.shared.mts` comment claimed.
- The rule as written told a reader to put anything reached through root-owned
  code — `core/` included — in `devDependencies`. That is wrong and would break
  the published package silently: the client builds externalize npm packages, so
  a published install resolves them from the root manifest, where
  devDependencies are absent. Placement (which manifest) and classification
  (which section) are now stated as separate questions, the second following
  from who consumes the package at runtime.

`yaml`'s runtime classification is left alone and called out instead: moving it
changes what ships, which is not a docs change.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01HDdo1rNRVQnVRRdsqSrvG3

README.md

@@ -66,7 +66,7 @@ npm install     # root install; postinstall cascades into every client
 
 The cascade (`scripts/install-clients.mjs`) is dev-only — it exits early when the package is installed as a dependency, and the published tarball ships only each client's `build/`, so end users are unaffected. Set `INSPECTOR_SKIP_CLIENT_INSTALL=1` to skip it.
 
-**Where a dependency is declared.** The MCP SDK packages (`@modelcontextprotocol/client`, `core`, `server`, `server-legacy`, `ext-apps`) live in the **root** `package.json` only — never in a client's. Node resolution walks up, so the root install is on every client's chain, and the root manifest is already what the published tarball resolves against. Declaring them per client installs a second copy that can drift from the root's, which is how two versions of `ext-apps` (and of the transitive v1 `@modelcontextprotocol/sdk`) ended up in the tree before [#1970](https://github.com/modelcontextprotocol/inspector/issues/1970) — and a second copy of `client`/`core` is the failure `vitest.shared.mts` carries a `dedupe` workaround for. The same holds for anything used only by root-owned code with no manifest of its own: `express` (imported by `test-servers/src`) and `yaml` are root devDependencies, resolved from the root by `vitest.shared.mts`.
+**Where a dependency is declared.** The MCP SDK packages (`@modelcontextprotocol/client`, `core`, `server`, `server-legacy`, `ext-apps`) live in the **root** `package.json` only — never in a client's. Node resolution walks up, so the root install is on every client's chain, and the root manifest is already what the published tarball resolves against. Declaring them per client installs a second copy that can drift from the root's, which is how two versions of `ext-apps` (and of the transitive v1 `@modelcontextprotocol/sdk`) ended up in the tree before [#1970](https://github.com/modelcontextprotocol/inspector/issues/1970) — and a second copy of `client`/`core` is the failure `vitest.shared.mts` carries a `dedupe` workaround for. The same root-only placement holds for anything reached solely through root-owned code with no manifest of its own (`test-servers/src`, `core/`), and `vitest.shared.mts` aliases those to the repo root — `express` and `yaml`, both reached through `test-servers/src`, are the two today. **Whether such a package is a `dependency` or a `devDependency` follows from who consumes it at runtime, not from where it is declared:** anything `core/` imports at runtime must be a root **`dependency`**, because the client builds externalize npm packages and a published install resolves them from the root manifest, where devDependencies are absent. `express` is test-only and is a devDependency; `yaml` currently sits in `dependencies`.
 
 ## Running during development