fix: address Copilot review round 1 on #2318

- fetchTracking: count NDJSON streams line by line instead of leaving
  them at zero forever; justify the detached watcher promise; document
  that a partial SSE block at end-of-stream is dropped, as the SDK's own
  parser (no flush) and the SSE spec drop it.
- uncapturedBodyNote: case-insensitive content-type lookup, and a
  stream label (SSE / NDJSON) for the Network badge.
- InspectorClient: `openedAt` is when the response headers arrived, not
  when the GET went out; the snapshot copies its request records; a
  request the transport failed to send is rolled back out of the
  unanswered set via a new `trackSendFailure` callback; a raw-wire
  timeout is built as the SDK's own timeout shape and annotated the
  same way, so callers see one kind of timeout.
- Remote session storage revives the nested `stream.closedAt` Date.
- Hook test models a legacy double with `Object.defineProperty`, not a
  double cast.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01APKSYHGxXBUpnR7ErFiLJn
Signed-off-by: cliffhall <cliff@futurescale.com>

core/mcp/remote/sessionStorage.ts

@@ -119,7 +119,10 @@ export class RemoteInspectorClientStorage implements InspectorClientStorage {
 
     const data = (await res.json()) as InspectorClientSessionState;
 
-    // Deserialize state (convert ISO strings back to Date objects)
+    // Deserialize state (convert ISO strings back to Date objects). The
+    // nested `stream.closedAt` is a Date too, and `JSON.stringify` turned it
+    // into an ISO string on the way out; left as a string it would fail the
+    // `getTime()` every consumer of the type performs (#2318).
     return {
       ...data,
       fetchRequests: data.fetchRequests.map((req) => ({
@@ -130,6 +133,9 @@ export class RemoteInspectorClientStorage implements InspectorClientStorage {
             : req.timestamp instanceof Date
               ? req.timestamp
               : new Date(req.timestamp),
+        ...(req.stream?.closedAt !== undefined && {
+          stream: { ...req.stream, closedAt: new Date(req.stream.closedAt) },
+        }),
       })),
     };
   }