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')} />

apps/desktop/src/i18n/ja.ts

@@ -1430,7 +1430,7 @@ export const ja = defineLocale({
     },
     startingSignIn: provider => `${provider} のサインインを開始中...`,
     verifyingCode: provider => `${provider} でコードを確認中...`,
-    connectedProvider: provider => `${provider} が接続されました。`,
+    connectedProvider: provider => `${provider} が接続されました`,
     connectedPicking: provider => `${provider} が接続されました。デフォルトモデルを選択中...`,
     signInFailed: 'サインインに失敗しました。再試行してください。',
     pickDifferentProvider: '別のプロバイダーを選択',
@@ -1456,7 +1456,7 @@ export const ja = defineLocale({
     free: '無料',
     price: (input, output) => `${input} 入力 / ${output} 出力 per Mtok`,
     change: '変更',
-    startChatting: 'チャットを始める',
+    startChatting: '始める',
     docs: provider => `${provider} ドキュメント`
   },
 

apps/desktop/src/i18n/zh-hant.ts

@@ -1391,7 +1391,7 @@ export const zhHant = defineLocale({
     },
     startingSignIn: provider => `正在為 ${provider} 啟動登入...`,
     verifyingCode: provider => `正在透過 ${provider} 驗證您的代碼...`,
-    connectedProvider: provider => `${provider} 已連線。`,
+    connectedProvider: provider => `${provider} 已連線`,
     connectedPicking: provider => `${provider} 已連線。正在選擇預設模型...`,
     signInFailed: '登入失敗，請重試。',
     pickDifferentProvider: '選擇其他提供方',
@@ -1417,7 +1417,7 @@ export const zhHant = defineLocale({
     free: '免費',
     price: (input, output) => `${input} 輸入 / ${output} 輸出 每 Mtok`,
     change: '變更',
-    startChatting: '開始聊天',
+    startChatting: '開始',
     docs: provider => `${provider} 文件`
   },
 

apps/desktop/src/i18n/zh.ts

@@ -1470,7 +1470,7 @@ export const zh: Translations = {
     },
     startingSignIn: provider => `正在为 ${provider} 启动登录...`,
     verifyingCode: provider => `正在通过 ${provider} 验证你的代码...`,
-    connectedProvider: provider => `${provider} 已连接。`,
+    connectedProvider: provider => `${provider} 已连接`,
     connectedPicking: provider => `${provider} 已连接。正在选择默认模型...`,
     signInFailed: '登录失败，请重试。',
     pickDifferentProvider: '选择其他提供方',
@@ -1494,7 +1494,7 @@ export const zh: Translations = {
     free: '免费',
     price: (input, output) => `${input} 输入 / ${output} 输出每 Mtok`,
     change: '更改',
-    startChatting: '开始对话',
+    startChatting: '开始',
     docs: provider => `${provider} 文档`
   },