fix(desktop): remember the manual update-check result across Settings open/close

The status was component state in the settings tab, so closing Settings
threw away "update available" and forced another check. Move it to a
module-level atom shared by the settings panel and the update toast.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01PPmy3tPq869XDW4njjVaKA

src/app/hooks/useTauriUpdater.ts

@@ -1,4 +1,5 @@
-import { useState, useCallback } from 'react';
+import { useCallback } from 'react';
+import { atom, useAtom } from 'jotai';
 
 type TauriInternals = { invoke: (cmd: string, args?: Record<string, unknown>) => Promise<unknown> };
 const tauriInvoke = (): TauriInternals['invoke'] | undefined =>
@@ -12,9 +13,16 @@ type UpdateStatus =
   | { state: 'installing' }
   | { state: 'error'; message: string };
 
+// Module-level so the result of a manual "Check for updates" survives closing
+// and reopening Settings (it used to be component state, so the "update
+// available" answer was thrown away with the tab and had to be re-checked).
+// A transient 'checking'/'installing' state is reset if the tab unmounts
+// mid-request by the resolve/reject below, so nothing gets stuck.
+const updateStatusAtom = atom<UpdateStatus>({ state: 'idle' });
+
 export function useTauriUpdater() {
   const isTauri = !!tauriInvoke();
-  const [status, setStatus] = useState<UpdateStatus>({ state: 'idle' });
+  const [status, setStatus] = useAtom(updateStatusAtom);
 
   const check = useCallback(async () => {
     const invoke = tauriInvoke();
@@ -30,7 +38,7 @@ export function useTauriUpdater() {
     } catch (e) {
       setStatus({ state: 'error', message: String(e) });
     }
-  }, []);
+  }, [setStatus]);
 
   const install = useCallback(async () => {
     const invoke = tauriInvoke();
@@ -45,7 +53,7 @@ export function useTauriUpdater() {
     } catch (e) {
       setStatus({ state: 'error', message: String(e) });
     }
-  }, []);
+  }, [setStatus]);
 
   return { isTauri, status, check, install };
 }