feat(web): migrate OAuth store to shared /store API (RemoteOAuthStorage parity) (closes #1548)

Migrate the web client's OAuth storage from BrowserOAuthStorage
(sessionStorage) to RemoteOAuthStorage, which POSTs through the backend's
/api/storage/oauth route to ~/.mcp-inspector/storage/oauth.json (mode 0600).
A credential obtained in the browser is now the same blob the TUI/CLI read
on the same host, giving web ⇄ TUI ⇄ CLI parity (Wave 1 of #1579).

Core (shared with TUI/CLI):
- OAuthStorageBase now drives a single async hydration (`ready()`,
  `getHydrationError()`); every post-redirect read (getClientInformation,
  getTokens, getCodeVerifier, getServerMetadata, getIdpSession) and every
  save awaits it so a late hydration merge cannot clobber a fresh write.
  getCodeVerifier/getServerMetadata become async; the store is created with
  skipHydration:true so there is no auto-hydration to race the explicit one.
- store.ts adds normalizeServerUrl so a token saved under
  https://Example.com/mcp is found when the CLI asks for
  https://example.com/mcp/; getServerState falls back to the raw key.
- remote-storage adapter POSTs with keepalive so the write survives the
  OAuth authorize redirect, surfaces swallowed persist failures, and gives
  richer read/write error messages.
- generateOAuthState throws instead of silently degrading to Math.random.
- NodeOAuthStorage honors MCP_INSPECTOR_OAUTH_STATE_PATH for isolated
  fixtures. Provider codeVerifier()/getServerMetadata() + the EMA idpOidc and
  connection-state readers await the now-async storage.

Web:
- environmentFactory + a new shared lib/remoteOAuthStorage accessor
  (memoized per {baseUrl, authToken}) wire RemoteOAuthStorage into the
  connection path, the EMA IdP hook, and the per-server "clear OAuth" action
  so all three share one in-memory view of oauth.json.

Tests: async-hydration + normalizeServerUrl suite, keepalive/error-path
coverage, and the sync→async migration across existing storage/provider/EMA
tests. Web validate + coverage gate + integration suite green; CLI/TUI/
launcher validate green.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01S3fTN8H3R8YV4yUGvZjYnX

core/auth/ema/idpOidc.ts

@@ -35,7 +35,7 @@ async function resolveIdpMetadata(
   fetchFn?: typeof fetch,
 ): Promise<OAuthMetadata> {
   const storageKey = idpOAuthStorageKey(issuer);
-  const cached = storage.getServerMetadata(storageKey);
+  const cached = await storage.getServerMetadata(storageKey);
   if (cached?.token_endpoint) {
     return cached;
   }
@@ -101,7 +101,7 @@ export async function completeIdpOidcAuthorization(params: {
 }> {
   const issuer = normalizeIdpIssuer(params.idp.issuer);
   const storageKey = idpOAuthStorageKey(issuer);
-  const metadata = params.storage.getServerMetadata(storageKey);
+  const metadata = await params.storage.getServerMetadata(storageKey);
   if (!metadata) {
     throw new Error("IdP OAuth metadata not found — restart EMA IdP login");
   }
@@ -111,7 +111,7 @@ export async function completeIdpOidcAuthorization(params: {
   if (!clientInformation) {
     throw new Error("IdP client information not found — restart EMA IdP login");
   }
-  const codeVerifier = params.storage.getCodeVerifier(storageKey);
+  const codeVerifier = await params.storage.getCodeVerifier(storageKey);
   if (!codeVerifier) {
     throw new Error("IdP PKCE verifier not found — restart EMA IdP login");
   }