Phase 1: Refactor all 16 element component interfaces to use MCP SDK types

Replace ad-hoc local type definitions in element components with real
MCP SDK types and Inspector wrapper types from core/mcp/types.ts:

Schema-typed primitives:
- LogLevelBadge: LogLevel → LoggingLevel (SDK)
- TransportBadge: "stdio"|"http" → ServerType (core), add sse/streamable-http
- TaskStatusBadge: local TaskStatus → SDK TaskStatus (working/input_required/...)
- ServerStatusIndicator: inline union → ConnectionStatus (core), "failed"→"error"

MCP wrapper consumers:
- AnnotationBadge: label+variant → facet+value with SDK Role type
- CapabilityItem: name:string → capability:keyof ServerCapabilities|ClientCapabilities
- LogEntry: flat props → entry:{receivedAt:Date, params:LoggingMessageNotification["params"]}
- MessageBubble: flat props → message:SamplingMessage|PromptMessage
- ProgressDisplay: flat props → params:ProgressNotification["params"]

Composite-input elements:
- ContentViewer: type+content+mimeType → block:ContentBlock (SDK discriminated union)
- InlineError: message+details → error:{message,data?}
- ConnectionToggle: checked+loading+onChange → status:ConnectionStatus+onConnect/onDisconnect

Also updates all group/screen/view consumers to keep the build green,
and renames CSS variable --inspector-status-failed → --inspector-status-error.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

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

@@ -6,7 +6,7 @@ import type { TaskCardProps } from "../TaskCard/TaskCard";
 const sampleTasks: TaskCardProps[] = [
   {
     taskId: "d0b22eba71fa36229ce5c4dfadeaa7de",
-    status: "running",
+    status: "working",
     method: "tools/call",
     target: "generate_report",
     progress: 80,
@@ -19,7 +19,7 @@ const sampleTasks: TaskCardProps[] = [
   },
   {
     taskId: "4100b5e0b0ed9cd0023330342d1bf647",
-    status: "waiting",
+    status: "input_required",
     method: "resources/read",
     target: "file:///data/report.csv",
     startedAt: "3/29/2026, 8:17:55 PM",

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

@@ -36,7 +36,7 @@ function formatCompletedTitle(count: number): string {
 }
 
 function isActiveStatus(status: string): boolean {
-  return status === "waiting" || status === "running";
+  return status === "working" || status === "input_required";
 }
 
 function matchesFilters(