SDK v2 migration (behavior-neutral, versionNegotiation: 'legacy') (#1624)

Migrate all three clients + core + test-servers from
@modelcontextprotocol/sdk@1.29 to SDK v2 (2.0.0-beta.4), keeping behavior
identical against legacy (2025-11-25) servers. Foundation for the SDK V2 +
New Spec stack.

Packages
- Split @modelcontextprotocol/sdk -> @modelcontextprotocol/client (Client,
  transports, OAuth, error taxonomy, protocol types) + core (Zod schemas);
  stdio -> client/stdio, Ajv -> client/validators/ajv. Test-servers ->
  @modelcontextprotocol/server (+ server-legacy/sse). Deterministic import
  rewrite (schemas -> core, everything else -> client); the codemod misroutes
  client code to /server so it was not used for path routing.
- new Client(..., { versionNegotiation: { mode: 'legacy' } }) — nothing
  2026-era goes on the wire.

Runtime (core/mcp/inspectorClient.ts)
- Error taxonomy: McpError -> ProtocolError, ErrorCode -> ProtocolErrorCode;
  RequestTimeout -> SdkError/SdkErrorCode.
- Handlers take method strings; task methods (tasks/*, notifications/tasks/*)
  use the 3-arg custom form (excluded from v2's spec-method set).
- Legacy tasks kept working (per project requirement): requestor tasks re-
  implemented over raw client.request + explicit deprecated schemas;
  experimental.tasks.callToolStream replaced by a local pollTaskToolCall
  async generator (with _progressHandlers revival so task-execution progress
  still reaches the caller). Receiver (server-initiated) tasks: the v2 Client
  validates a sampling/elicit handler result and rejects the legacy { task }
  response with -32602 — installReceiverTaskResponseBypass swaps the wrapped
  entry in the private _requestHandlers map for the task-augmented branch so
  { task } reaches the wire (fixes server-initiated sampling-via-task).
- Pagination: list verbs use raw client.request({method}, List*ResultSchema)
  for single-page behavior (v2's client.listX() auto-aggregate all pages).

Web / auth / apps
- Rename local JsonSchemaType -> InspectorFormSchema + add toFormSchema()
  structural narrowing at the SDK-schema -> form boundary.
- ext-apps still peers on SDK v1: one compat boundary with documented casts
  (remove when ext-apps#702 lands a v2 peer).
- OAuth provider saveClientInformation reconciled with v2's
  OAuthClientInformationContext; InvalidClientMetadataError re-homed as a
  local class (server-legacy/auth is not browser-safe).
- vitest.shared.mts dedupes @modelcontextprotocol/client+core to one copy so
  vi.mock intercepts the SUT's import.

Accepted v2 behavior changes (per #1624 / spec §9.2): unknown-tool call
rejects with -32602; cancellation is stream-abort (no guaranteed
notifications/cancelled frame); output-schema strictness restored via the
Inspector's own Ajv check on the default path.

npm run ci green: validate (web 3087 / cli 212 / tui 274 / launcher 5),
coverage (>=90 per-file, all clients), smoke (launcher/cli/web), storybook
(410).

Closes #1624

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

clients/web/src/components/groups/InlineSamplingRequest/InlineSamplingRequest.stories.tsx

@@ -2,7 +2,7 @@ import type { Meta, StoryObj } from "@storybook/react-vite";
 import type {
   CreateMessageRequestParams,
   CreateMessageResult,
-} from "@modelcontextprotocol/sdk/types.js";
+} from "@modelcontextprotocol/client";
 import { fn } from "storybook/test";
 import { InlineSamplingRequest } from "./InlineSamplingRequest";
 

clients/web/src/components/groups/InlineSamplingRequest/InlineSamplingRequest.test.tsx

@@ -3,7 +3,7 @@ import userEvent from "@testing-library/user-event";
 import type {
   CreateMessageRequestParams,
   CreateMessageResult,
-} from "@modelcontextprotocol/sdk/types.js";
+} from "@modelcontextprotocol/client";
 import { renderWithMantine, screen } from "../../../test/renderWithMantine";
 import { InlineSamplingRequest } from "./InlineSamplingRequest";
 

clients/web/src/components/groups/InlineSamplingRequest/InlineSamplingRequest.tsx

@@ -2,7 +2,7 @@ import { Badge, Button, Group, Paper, Stack, Text } from "@mantine/core";
 import type {
   CreateMessageRequestParams,
   CreateMessageResult,
-} from "@modelcontextprotocol/sdk/types.js";
+} from "@modelcontextprotocol/client";
 
 export interface InlineSamplingRequestProps {
   request: CreateMessageRequestParams;