feat: task 1.8 logout flow + cross-tab sync + strict tsconfig

- src/auth/logout.ts: performLogout({ queryClient, navigate? })
  orchestration. Calls store.logout(), clears query cache, navigates
  to /login. Server-call failures swallowed; local state still flips
  to anonymous.
- src/auth/cross-tab-sync.ts: startCrossTabSync(). Subscribes to the
  auth store and bumps trm-auth-version in localStorage on status
  transitions; listens for storage events and re-runs initialize()
  when another tab bumps. Idempotent via module-level guard. No-ops
  if localStorage is unavailable.
- src/ui/components/logout-button.tsx: <LogoutButton> wraps shadcn
  Button. Pass-through props but locks onClick / disabled / children.
  Local isLoggingOut for "Signing out..." indicator + double-click
  guard.
- src/auth/bootstrap.tsx: <AuthBootstrap> now calls startCrossTabSync()
  alongside the existing init steps. Single mount point.
- src/auth/index.ts: re-export performLogout + startCrossTabSync.
- src/routes/_authed/index.tsx: replaced the inline sign-out button
  with <LogoutButton />. The existing useEffect on 'anonymous' status
  handles navigation when cross-tab sync fires.

Bonus: tsconfig.app.json now has "strict": true. TanStack Router emits
a conditional-type error ("strictNullChecks must be enabled") in
editors when strict is off; tsc -b was lenient. Caught in 1.7's
review. Typecheck remained green after enabling.

src/ui/components/logout-button.tsx

@@ -0,0 +1,33 @@
+import { useState, type ComponentProps } from 'react';
+import { useQueryClient } from '@tanstack/react-query';
+import { useNavigate } from '@tanstack/react-router';
+import { performLogout } from '@/auth/logout';
+import { Button } from '@/ui/primitives/button';
+
+type ButtonProps = ComponentProps<typeof Button>;
+
+export type LogoutButtonProps = Omit<ButtonProps, 'onClick' | 'disabled' | 'children'>;
+
+export function LogoutButton({ variant = 'outline', ...rest }: LogoutButtonProps) {
+  const queryClient = useQueryClient();
+  const navigate = useNavigate();
+  const [isLoggingOut, setIsLoggingOut] = useState(false);
+
+  async function onClick() {
+    if (isLoggingOut) return;
+    setIsLoggingOut(true);
+    try {
+      await performLogout({ queryClient, navigate });
+    } catch {
+      // Even if the orchestration throws somewhere, the auth store is now
+      // anonymous and the user is signed out locally. Nothing useful to
+      // recover here.
+    }
+  }
+
+  return (
+    <Button variant={variant} onClick={onClick} disabled={isLoggingOut} {...rest}>
+      {isLoggingOut ? 'Signing out…' : 'Sign out'}
+    </Button>
+  );
+}