test: close ≥90% per-file coverage gaps for mid-session auth

The mid-session auth work passed `validate`/CI but failed the local-only
`npm run test:coverage` per-file gate (≥90% lines/statements/functions/
branches) on 12 files. Add targeted unit/integration tests so every changed
file clears the gate; annotate provably-dead defensive branches with justified
`/* v8 ignore */` comments rather than relaxing the gate.

Files brought to ≥90 on all four dimensions:
- core/auth: mcpAuth, oauthUx, utils, challenge, node/runner-interactive-oauth
- core/mcp: oauthManager, inspectorClient, node/authChallengeFetch,
  remote/remoteClientTransport, remote/node/{remote-session,server}
- clients/web/src/utils: oauthResume, browserTabVisibility

`npm run test:coverage` now passes (3575 tests, 0 threshold failures);
`npm run validate` green across all four clients.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DZyeWManYTvcXxjcrhxSQc

core/mcp/inspectorClient.ts

@@ -2529,8 +2529,7 @@ export class InspectorClient extends InspectorClientEventTarget {
           ),
         {
           method: "completion/complete",
-          toolName:
-            ref.type === "ref/prompt" ? ref.name : ref.uri,
+          toolName: ref.type === "ref/prompt" ? ref.name : ref.uri,
         },
       );
 
@@ -2941,6 +2940,7 @@ export class InspectorClient extends InspectorClientEventTarget {
         throw err;
       }
       const challenge = parseAuthChallengeFromError(err, context);
+      /* v8 ignore next 3 -- defensive: parseAuthChallengeFromError shares isAuthChallengeError's checks, so it always returns a truthy challenge once that guard passes */
       if (!challenge) {
         throw err;
       }
@@ -2994,7 +2994,10 @@ export class InspectorClient extends InspectorClientEventTarget {
    * Direct transports reconnect after token exchange so the live MCP session
    * picks up the new Bearer token (mirrors silent recovery reconnect).
    */
-  async completeOAuthFlow(authorizationCode: string, iss?: string): Promise<void> {
+  async completeOAuthFlow(
+    authorizationCode: string,
+    iss?: string,
+  ): Promise<void> {
     await this.ensureOAuthManager().completeOAuthFlow(authorizationCode, iss);
     if (this.usesDirectAuthRecovery()) {
       await this.reconnectAfterAuthRecovery();