feat(locale): derive the initial Settings language from the browser

A first visit resolved to Chinese regardless of the browser: LocaleService
read `dsh.locale` and fell straight back to `zh` when nothing was stored,
ignoring the languages the browser already states it reads.

The initial locale now resolves through three ordered sources — the persisted
preference, then `navigator` (first entry of the ordered language list whose
primary subtag names a shipped locale, so `zh-Hans-CN` -> zh and `en-GB` ->
en), then `FALLBACK_LOCALE`. An explicit choice still wins and nothing writes
the detected locale back to storage, so "has the user chosen?" stays a
question only the stored value answers.

Specs asserting the shipped Chinese copy now state the browser they assume:
the web e2e scenarios open their page with `locale: ZH_BROWSER_LOCALE`, and
package specs pin it through the new `pinBrowserLanguages` test helper.
`settings-chrome.e2e.ts` gains an English-browser scenario as the
assembled-app proof.

packages/client/locale/tests/apply.spec.ts

@@ -2,7 +2,7 @@
  * Language row registration, snapshot projection into the row store, and
  * recovery after an HMR collapse of the declaring entry. */
 import { Context } from 'cordis'
-import { describe, expect, it } from 'vitest'
+import { afterEach, beforeEach, describe, expect, it, vi } from 'vitest'
 import { SlotsService } from '@deepseek-ai/dsh-client-runtime/client'
 import { apply, inject, SETTINGS_NS } from '@deepseek-ai/dsh-client-locale/client'
 import type { LanguageRowInjected, LocaleService } from '@deepseek-ai/dsh-client-locale/client'
@@ -36,6 +36,16 @@ function faceOf(slots: SlotsService) {
 }
 
 describe('locale apply', () => {
+  // A fresh service opens in the browser's language, so these wiring specs
+  // pin one to keep their zh baseline independent of the test environment.
+  beforeEach(() => {
+    vi.stubGlobal('navigator', { languages: ['zh-CN'], language: 'zh-CN' })
+  })
+
+  afterEach(() => {
+    vi.unstubAllGlobals()
+  })
+
   it('declares the slot service', () => {
     expect(inject).toEqual(['slots'])
   })

packages/client/locale/tests/locale.spec.ts

@@ -1,5 +1,5 @@
 // @vitest-environment jsdom
-import { beforeEach, describe, expect, it, vi } from 'vitest'
+import { afterEach, beforeEach, describe, expect, it, vi } from 'vitest'
 import { Context } from 'cordis'
 import type { LocaleSnapshot } from '@deepseek-ai/dsh-client-locale/client'
 import { LocaleService, STORAGE_KEY } from '@deepseek-ai/dsh-client-locale/client'
@@ -11,9 +11,20 @@ const make = (): { ctx: Context; svc: LocaleService; events: LocaleSnapshot[] }
   return { ctx, svc: new LocaleService(ctx), events }
 }
 
+/** Pin the browser environment a fresh service reads its initial locale from. */
+const stubLanguages = (...tags: string[]): void => {
+  vi.stubGlobal('navigator', { languages: tags, language: tags[0] ?? '' })
+}
+
 describe('LocaleService', () => {
   beforeEach(() => {
     localStorage.clear()
+    // A Chinese browser is the baseline these specs assert their zh state on.
+    stubLanguages('zh-CN')
+  })
+
+  afterEach(() => {
+    vi.unstubAllGlobals()
   })
 
   it('translates through the active-locale -> zh -> key chain', () => {
@@ -132,23 +143,45 @@ describe('LocaleService', () => {
     expect(() => { svc.setLocale('fr') }).toThrow('not registered')
   })
 
-  it('restores a persisted locale and falls back to zh on garbage', () => {
+  it('restores a persisted locale over the browser language, and garbage reads as no preference', () => {
     localStorage.setItem(STORAGE_KEY, 'en')
     expect(make().svc.getLocale().active).toBe('en')
     localStorage.setItem(STORAGE_KEY, 'fr')
     expect(make().svc.getLocale().active).toBe('zh')
   })
 
-  it('runs without localStorage (node boots): defaults on read, no-op on write', () => {
+  it('opens in the browser language when nothing is persisted, matching regional variants on their primary subtag', () => {
+    stubLanguages('en-GB', 'zh-CN')
+    expect(make().svc.getLocale().active).toBe('en')
+    stubLanguages('zh-Hant-TW')
+    expect(make().svc.getLocale().active).toBe('zh')
+    // An unshipped language walks the list to the first one this app ships.
+    stubLanguages('fr-FR', 'en-US')
+    expect(make().svc.getLocale().active).toBe('en')
+    // Only `language` populated (browsers that expose no ordered list).
+    vi.stubGlobal('navigator', { languages: [], language: 'en-US' })
+    expect(make().svc.getLocale().active).toBe('en')
+    // No shipped language anywhere in the browser's preferences: zh remains
+    // the product default rather than an arbitrary near-match.
+    stubLanguages('fr-FR', 'de')
+    expect(make().svc.getLocale().active).toBe('zh')
+  })
+
+  it('runs without localStorage or navigator (node boots): defaults on read, no-op on write', () => {
     vi.stubGlobal('localStorage', undefined)
-    try {
-      const { svc } = make()
-      expect(svc.getLocale().active).toBe('zh')
-      svc.setLocale('en')
-      expect(svc.getLocale().active).toBe('en')
-    } finally {
-      vi.unstubAllGlobals()
-    }
+    vi.stubGlobal('navigator', undefined)
+    const { svc } = make()
+    expect(svc.getLocale().active).toBe('zh')
+    svc.setLocale('en')
+    expect(svc.getLocale().active).toBe('en')
+  })
+
+  it('keeps the browser language out of the way once a preference exists', () => {
+    stubLanguages('en-US')
+    const { svc } = make()
+    svc.setLocale('zh')
+    expect(localStorage.getItem(STORAGE_KEY)).toBe('zh')
+    expect(make().svc.getLocale().active).toBe('zh')
   })
 
   it('exposes the two shipped locales with self-described labels', () => {