feat(09-05): ThemeSessionBridge + ThemeToggle write-through to /api/me/theme

- Create ThemeSessionBridge.tsx: useEffect compares session.user.theme to
  next-themes value; calls setTheme(serverTheme) on mismatch; validates
  against 3-string allowlist ('light'|'dark'|'system'); renders null
- Mount <ThemeSessionBridge /> as first child of <AuthProvider> in app/layout.tsx
- Modify ThemeToggle: writeTheme() calls setTheme() then fire-and-forget
  PUT /api/me/theme; silent catch for network errors (best-effort desktop UX)

components/theme-toggle.tsx

@@ -15,6 +15,21 @@ import {
 export function ThemeToggle() {
   const { setTheme, theme } = useTheme()
 
+  // Write the new theme choice through to the server so session.user.theme
+  // stays canonical. Fire-and-forget — ThemeSessionBridge re-syncs from
+  // session on next session refresh if the request fails.
+  const writeTheme = (next: 'light' | 'dark' | 'system') => {
+    setTheme(next)
+    fetch('/api/me/theme', {
+      method: 'PUT',
+      headers: { 'Content-Type': 'application/json' },
+      body: JSON.stringify({ theme: next }),
+    }).catch(() => {
+      // Silent fail on network error — the desktop affordance is best-effort.
+      // The mobile profile Theme section is the explicit-error UX.
+    })
+  }
+
   return (
     <DropdownMenu>
       <DropdownMenuTrigger asChild>
@@ -25,15 +40,15 @@ export function ThemeToggle() {
         </Button>
       </DropdownMenuTrigger>
       <DropdownMenuContent align="end">
-        <DropdownMenuItem onClick={() => setTheme("light")}>
+        <DropdownMenuItem onClick={() => writeTheme("light")}>
           <Sun className="mr-2 h-4 w-4" />
           <span>Light</span>
         </DropdownMenuItem>
-        <DropdownMenuItem onClick={() => setTheme("dark")}>
+        <DropdownMenuItem onClick={() => writeTheme("dark")}>
           <Moon className="mr-2 h-4 w-4" />
           <span>Dark</span>
         </DropdownMenuItem>
-        <DropdownMenuItem onClick={() => setTheme("system")}>
+        <DropdownMenuItem onClick={() => writeTheme("system")}>
           <Monitor className="mr-2 h-4 w-4" />
           <span>System</span>
         </DropdownMenuItem>