fix(sidebar): require admin role for Schedule task and debounce search input (#1243)

The right-click Schedule task menu item and its keyboard shortcut were gated
only on isPaid, but the backend write routes under /api/scheduled-tasks
enforce requireAdmin + requirePaid on every action. Non-admin Skipper or
Admiral users would see the menu item and hit a 403 on click. The frontend
now mirrors the backend by gating Schedule task on isPaid && isAdmin so the
affordance only renders for users whose action will actually succeed.

Also adds a 120ms keystroke debounce to the sidebar search input. The
useStackListState filter rebuild was previously running on every keystroke
because <Command shouldFilter={false}> disables cmdk's own filter and the
existing 250ms timer only debounces state-invalidate events. Visible input
stays immediate via local state; the debounced emit drives the filter pass.

Adds a regression guard that /api/stacks/statuses is short-circuited by the
remote-node proxy (covers the sidebar status poll path) and updates the
sidebar feature docs to reflect the admin role requirement on Schedule task.

docs/features/sidebar.mdx

@@ -85,7 +85,7 @@ Right-click any stack (or open the kebab that appears on hover) for its context
 - **Destructive**: **Delete**.
 
 <Note>
-  **Auto-Heal** and **Schedule task** require a **Skipper** or **Admiral** license.
+  **Auto-Heal** requires a **Skipper** or **Admiral** license. **Schedule task** requires a **Skipper** or **Admiral** license and an **admin** role.
 </Note>
 
 <Frame>
@@ -143,4 +143,7 @@ The footer surfaces the most recent stack lifecycle event on the node. Each tick
   <Accordion title="The filter chips disappeared from the sidebar">
     Click the **+** icon to the right of the search box to bring them back. The chip row collapses to a thin **−** / **+** toggle, and the state is remembered in your browser, so an earlier collapse persists across reloads until you expand it again.
   </Accordion>
+  <Accordion title="Schedule task is missing from the right-click menu">
+    Scheduling requires a **Skipper** or **Admiral** license and an **admin** role. Ask an admin on this node to schedule the task for you, or sign in with an admin account.
+  </Accordion>
 </AccordionGroup>