feat(11-04): create GroupBadge component

- Built-in variant: Badge secondary, no dismiss, hover:bg-accent/30
- Custom variant: Badge outline, X dismiss button with spinner, hover:bg-accent/50
- Tooltip on both variants showing name · built-in · N skills or name · N skills
- text-sm font-semibold typography per UI-SPEC (no font-bold or font-medium)

ui/src/components/GroupBadge.tsx

@@ -0,0 +1,82 @@
+import { X, Loader2 } from "lucide-react";
+import { Badge } from "@/components/ui/badge";
+import { Tooltip, TooltipContent, TooltipTrigger } from "@/components/ui/tooltip";
+import { cn } from "@/lib/utils";
+
+type GroupBadgeProps = {
+  name: string;
+  isBuiltin: boolean;
+  skillCount?: number;
+  description?: string | null;
+  onRemove?: () => void;
+  removing?: boolean;
+};
+
+export function GroupBadge({
+  name,
+  isBuiltin,
+  skillCount,
+  description: _description,
+  onRemove,
+  removing = false,
+}: GroupBadgeProps) {
+  const tooltipText = isBuiltin
+    ? `${name} · built-in${skillCount != null ? ` · ${skillCount} skills` : ""}`
+    : `${name}${skillCount != null ? ` · ${skillCount} skills` : ""}`;
+
+  if (isBuiltin) {
+    return (
+      <Tooltip>
+        <TooltipTrigger asChild>
+          <Badge
+            variant="secondary"
+            className={cn(
+              "cursor-default select-none text-sm font-semibold",
+              "hover:bg-accent/30",
+              "focus-visible:ring-ring focus-visible:ring-[3px]",
+            )}
+          >
+            {name}
+          </Badge>
+        </TooltipTrigger>
+        <TooltipContent side="top">{tooltipText}</TooltipContent>
+      </Tooltip>
+    );
+  }
+
+  return (
+    <Tooltip>
+      <TooltipTrigger asChild>
+        <Badge
+          variant="outline"
+          className={cn(
+            "cursor-default select-none gap-1 text-sm font-semibold",
+            "hover:bg-accent/50",
+            "focus-visible:ring-ring focus-visible:ring-[3px]",
+          )}
+        >
+          {name}
+          {onRemove && (
+            <button
+              type="button"
+              aria-label={`Remove ${name}`}
+              disabled={removing}
+              onClick={(e) => {
+                e.stopPropagation();
+                onRemove();
+              }}
+              className="ml-0.5 rounded-full p-0.5 transition-colors hover:bg-accent disabled:cursor-not-allowed disabled:opacity-50"
+            >
+              {removing ? (
+                <Loader2 className="h-3 w-3 animate-spin" />
+              ) : (
+                <X className="h-3 w-3" />
+              )}
+            </button>
+          )}
+        </Badge>
+      </TooltipTrigger>
+      <TooltipContent side="top">{tooltipText}</TooltipContent>
+    </Tooltip>
+  );
+}