chore: upgrade the MCP TypeScript SDK from 2.0.0-beta.5 to 2.0.0

The SDK shipped 2.0.0 final on 2026-07-27. Shipping the Inspector against a
prerelease of its core protocol library is a supply-chain and reproducibility
liability we no longer have a reason to carry: a beta is eligible for unpublish
and deprecation in a way a stable release is not.

Bumped in the root package.json only — client, core, server, server-legacy.
Node resolution walks up, so the root install already serves every client; a
per-client declaration would install a second copy that drifts from it (#1970).
Verified after install: one copy of each at 2.0.0, no clients/*/node_modules/
@modelcontextprotocol/* at all. ext-apps is a separate package on its own ^1.7.4
line and is untouched.

The beta.5 → 2.0.0 delta is seven commits. Reviewed each for call-site impact:

  - core/src/schemas.ts (+16/-16) is doc-comment only — every hunk rewrites a
    spec URL from a commit-pinned GitHub blob to the published 2026-07-28 page.
    No schema surface change, so nothing in core/mcp or core/json is affected.
  - client 2.0.0 wants zod ^4.2.0; we are on ^4.4.3, so no zod move and no risk
    of the #1896 dual-copy tsc heap blowup. verify:dep-lockstep stays green and
    the lockfile delta is exactly the four packages with no transitive churn.
  - fix(validators) honors declared draft-07/06 JSON Schema dialects instead of
    rejecting them, which can only widen the set of tool schemas we accept.
  - The SSE keep-alive and legacyWrap changes are server-side, exercised by the
    test servers rather than by client code.

The one change with real behavioral reach is #2564: the negotiation probe now
classifies HTTP 401/403 as an auth failure instead of legacy-era evidence. That
is the upstream fix #1807 is blocked on, and it is left for that issue — the
directAuthRecovery clause in inspectorClient.ts still intercepts the challenge
before the classifier sees it, so this bump does not change connect behavior.
#1807 can now delete the workaround and lean on the SDK verdict, but doing it
here would smuggle an auth change into a dependency bump.

Also corrected the two auth as-built specs, which still claimed beta.4 —
already stale before this change. v2_new_spec_impact.md is deliberately left
alone: it is a dated pre-upgrade analysis, and editing its premises would
rewrite the record rather than update it.

npm run ci passes end to end: validate, the per-file >=90 coverage gate,
verify:build-gate, all six smokes (including web:app driving connect -> open
app -> data-app-status="ready"), and 472 Storybook tests.

Closes #1988

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

specification/v2_auth_hardening.md

@@ -6,7 +6,7 @@
 
 As-built status for aligning Inspector with the **authorization hardening** SEPs in the MCP **`2026-07-28`** release — tracked by [#1527](https://github.com/modelcontextprotocol/inspector/issues/1527).
 
-Inspector is on `@modelcontextprotocol/client` **2.0.0-beta.4**. Connect-time standard OAuth is delegated to SDK `auth()`; Inspector owns storage, callbacks, remoting, EMA host flow, and mid-session UX. See [SDK consolidation](v2_auth_sdk_consolidation.md).
+Inspector is on `@modelcontextprotocol/client` **2.0.0**. Connect-time standard OAuth is delegated to SDK `auth()`; Inspector owns storage, callbacks, remoting, EMA host flow, and mid-session UX. See [SDK consolidation](v2_auth_sdk_consolidation.md).
 
 **Policy:** SEP behavior that can be automated is covered (or should be covered) by unit/integration tests. Hosted-IdP smoke in [v2_auth_smoke_testing.md](v2_auth_smoke_testing.md) is complementary for real providers — it is **not** required for every SEP once CI covers the requirement.