fix: restore reliable update flow across sidebar and mobile

Show Update button in sidebar only when an update is available
Support update button on mobile sidebar and remove duplicate mobile Settings entry
Force desktop Tauri recheck and preflight before download to avoid missing pending updates

packages/ui/src/components/session/sidebar/SidebarFooter.tsx

@@ -1,16 +1,25 @@
 import React from 'react';
 import { RiInformationLine, RiQuestionLine, RiSettings3Line } from '@remixicon/react';
+import { Button } from '@/components/ui/button';
 import { Tooltip, TooltipContent, TooltipTrigger } from '@/components/ui/tooltip';
 
 type Props = {
   onOpenSettings: () => void;
   onOpenShortcuts: () => void;
   onOpenAbout: () => void;
+  onOpenUpdate: () => void;
+  showUpdateButton?: boolean;
 };
 
 const footerButtonClassName = 'inline-flex h-8 w-8 items-center justify-center rounded-md text-muted-foreground hover:bg-interactive-hover/50 hover:text-foreground focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-primary/50';
 
-export function SidebarFooter({ onOpenSettings, onOpenShortcuts, onOpenAbout }: Props): React.ReactNode {
+export function SidebarFooter({
+  onOpenSettings,
+  onOpenShortcuts,
+  onOpenAbout,
+  onOpenUpdate,
+  showUpdateButton = true,
+}: Props): React.ReactNode {
   return (
     <div className="flex shrink-0 items-center justify-start gap-1 px-2.5 py-2">
       <Tooltip>
@@ -37,6 +46,17 @@ export function SidebarFooter({ onOpenSettings, onOpenShortcuts, onOpenAbout }:
         </TooltipTrigger>
         <TooltipContent side="top" sideOffset={4}><p>About OpenChamber</p></TooltipContent>
       </Tooltip>
+      {showUpdateButton ? (
+        <Button
+          type="button"
+          variant="default"
+          size="xs"
+          className="ml-auto border-[var(--status-info-border)] bg-[var(--status-info-background)] text-[var(--status-info)] hover:bg-[var(--status-info-background)]/80 hover:text-[var(--status-info)]"
+          onClick={onOpenUpdate}
+        >
+          Update
+        </Button>
+      ) : null}
     </div>
   );
 }