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/TaskControls/TaskControls.stories.tsx

@@ -27,6 +27,6 @@ export const WithSearch: Story = {
 
 export const WithFilter: Story = {
   args: {
-    statusFilter: "running",
+    statusFilter: "working",
   },
 };

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

@@ -2,8 +2,8 @@ import { Button, Group, Select, Stack, TextInput, Title } from "@mantine/core";
 import type { TaskStatus } from "../TaskCard/TaskCard";
 
 const STATUS_OPTIONS: TaskStatus[] = [
-  "waiting",
-  "running",
+  "working",
+  "input_required",
   "completed",
   "failed",
   "cancelled",