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/TaskCard/TaskCard.stories.tsx

@@ -14,10 +14,10 @@ const meta: Meta<typeof TaskCard> = {
 export default meta;
 type Story = StoryObj<typeof TaskCard>;
 
-export const Running: Story = {
+export const Working: Story = {
   args: {
     taskId: "d0b22eba71fa36229ce5c4dfadeaa7de",
-    status: "running",
+    status: "working",
     method: "tools/call",
     target: "generate_report",
     progress: 80,
@@ -28,10 +28,10 @@ export const Running: Story = {
   },
 };
 
-export const Waiting: Story = {
+export const InputRequired: Story = {
   args: {
     taskId: "4100b5e0b0ed9cd0023330342d1bf647",
-    status: "waiting",
+    status: "input_required",
     method: "resources/read",
     target: "file:///data/report.csv",
     startedAt: "3/29/2026, 8:17:55 PM",
@@ -84,7 +84,7 @@ export const Cancelled: Story = {
 export const Collapsed: Story = {
   args: {
     taskId: "d0b22eba71fa36229ce5c4dfadeaa7de",
-    status: "running",
+    status: "working",
     method: "tools/call",
     target: "generate_report",
     progress: 80,