feat(ui): add auth pages, company rail, inbox redesign, and page improvements

Add Auth sign-in/sign-up page and InviteLanding page for invite acceptance.
Add CloudAccessGate that checks deployment mode and redirects to /auth when
session is required. Add CompanyRail with drag-and-drop company switching.
Add MarkdownBody prose renderer. Redesign Inbox with category filters and
inline join-request approval. Refactor AgentDetail to overview/configure/runs
views with claude-login support. Replace navigate() anti-patterns with <Link>
components in Dashboard and MetricCard. Add live-run indicators in sidebar
agents. Fix LiveUpdatesProvider cache key resolution for issue identifiers.
Add auth, health, and access API clients.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

ui/src/components/SidebarNavItem.tsx

@@ -11,6 +11,7 @@ interface SidebarNavItemProps {
   badge?: number;
   badgeTone?: "default" | "danger";
   alert?: boolean;
+  liveCount?: number;
 }
 
 export function SidebarNavItem({
@@ -21,6 +22,7 @@ export function SidebarNavItem({
   badge,
   badgeTone = "default",
   alert = false,
+  liveCount,
 }: SidebarNavItemProps) {
   const { isMobile, setSidebarOpen } = useSidebar();
 
@@ -45,6 +47,15 @@ export function SidebarNavItem({
         )}
       </span>
       <span className="flex-1 truncate">{label}</span>
+      {liveCount != null && liveCount > 0 && (
+        <span className="ml-auto flex items-center gap-1.5">
+          <span className="relative flex h-2 w-2">
+            <span className="animate-ping absolute inline-flex h-full w-full rounded-full bg-blue-400 opacity-75" />
+            <span className="relative inline-flex rounded-full h-2 w-2 bg-blue-500" />
+          </span>
+          <span className="text-[11px] font-medium text-blue-400">{liveCount} live</span>
+        </span>
+      )}
       {badge != null && badge > 0 && (
         <span
           className={cn(