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/elements/LogLevelBadge/LogLevelBadge.tsx

@@ -1,11 +1,11 @@
 import { Badge, useComputedColorScheme } from "@mantine/core";
-import type { LogLevel } from "../LogEntry/LogEntry";
+import type { LoggingLevel } from "@modelcontextprotocol/sdk/types.js";
 
 export interface LogLevelBadgeProps {
-  level: LogLevel;
+  level: LoggingLevel;
 }
 
-const levelColor: Record<LogLevel, string> = {
+const levelColor: Record<LoggingLevel, string> = {
   debug: "gray",
   info: "blue",
   notice: "teal",
@@ -16,7 +16,7 @@ const levelColor: Record<LogLevel, string> = {
   emergency: "red",
 };
 
-const boldLevels: Set<LogLevel> = new Set(["alert", "emergency"]);
+const boldLevels: Set<LoggingLevel> = new Set(["alert", "emergency"]);
 
 export function LogLevelBadge({ level }: LogLevelBadgeProps) {
   const colorScheme = useComputedColorScheme();