docs(desktop): add DESIGN.md design-system guide + close two consistency gaps (#40823)

Codify the desktop overlay/design conventions in apps/desktop/DESIGN.md:
surfaces & elevation (shadow-nous + --stroke-nous), stroke/color tokens, the
single Button (variants/sizes, no per-call overrides), shared form controls
(controlVariants / SearchField / SegmentedControl / Switch), flat layout
(PAGE_INSET_X, OverlaySplitLayout, ListRow, no card-in-card), feedback states
(Loader / ErrorState / LogView / EmptyState), BrandMark, motion, i18n, and the
nanostore state model. Ends with a pre-merge checklist.

Two fixes so the doc isn't aspirational:
- brand-mark: rounded-md + overflow-hidden (doc says "softly rounded")
- i18n ja/zh/zh-hant: mirror en's "Begin" + drop trailing period on
  connectedProvider (doc says update all locales together)

apps/desktop/src/components/brand-mark.tsx

@@ -3,11 +3,14 @@ import { cn } from '@/lib/utils'
 const assetPath = (path: string) => `${import.meta.env.BASE_URL}${path.replace(/^\/+/, '')}`
 
 // Brand badge: nous-girl mark on a white tile, identical in light/dark.
-// Fills the tile (no padding/radius); size via className (default size-14).
+// Fills the tile (softly rounded); size via className (default size-14).
 export function BrandMark({ className, ...props }: React.ComponentProps<'span'>) {
   return (
     <span
-      className={cn('inline-flex size-14 shrink-0 items-center justify-center bg-white', className)}
+      className={cn(
+        'inline-flex size-14 shrink-0 items-center justify-center overflow-hidden rounded-md bg-white',
+        className
+      )}
       {...props}
     >
       <img alt="" className="size-full object-contain" src={assetPath('nous-girl.jpg')} />