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/src/client/index.ts

@@ -83,7 +83,7 @@ declare module 'cordis' {
   }
 }
 
-/** Fallback locale consulted after the active locale misses (also the default). */
+/** Fallback locale consulted after the active locale misses (also the last-resort initial locale). */
 export const FALLBACK_LOCALE: LocaleId = 'zh'
 
 /** Shared namespace for shell-level texts. */
@@ -123,7 +123,7 @@ export class LocaleService {
    */
   constructor(ctx: Context) {
     this.ctx = ctx
-    this.snapshot = Object.freeze({ active: restorePreference(), locales: LOCALES, revision: 0 })
+    this.snapshot = Object.freeze({ active: resolveInitialLocale(), locales: LOCALES, revision: 0 })
   }
 
   /**
@@ -288,17 +288,45 @@ export class LocaleService {
   }
 }
 
-/** Read the persisted locale id; unknown or unreadable values fall back to zh. */
-function restorePreference(): LocaleId {
+/**
+ * The locale a fresh service opens with: an explicit preference the user
+ * already chose wins over the browser's own language, which in turn wins over
+ * {@link FALLBACK_LOCALE} (non-browser boots and browsers set to a language
+ * this app does not ship).
+ */
+function resolveInitialLocale(): LocaleId {
+  return restorePreference() ?? detectBrowserLocale() ?? FALLBACK_LOCALE
+}
+
+/** Read the persisted locale id; unknown or unreadable values read as no preference. */
+function restorePreference(): LocaleId | undefined {
   // Non-browser runs (node e2e booting the client tree) have no localStorage.
-  if (typeof localStorage === 'undefined') return FALLBACK_LOCALE
+  if (typeof localStorage === 'undefined') return undefined
   try {
     const stored = localStorage.getItem(STORAGE_KEY)
     if (stored === 'zh' || stored === 'en') return stored
   } catch {
-    // Storage access can throw (privacy mode); the default below covers it.
+    // Storage access can throw (privacy mode); an unreadable store simply
+    // records no preference, and the browser language decides instead.
   }
-  return FALLBACK_LOCALE
+  return undefined
+}
+
+/**
+ * The first shipped locale the browser asks for, matched on the primary
+ * subtag so every regional variant lands on its language (`zh-Hans-CN` -> zh,
+ * `en-GB` -> en). `navigator.language` trails the ordered `languages` list
+ * because a browser may expose only the former.
+ */
+function detectBrowserLocale(): LocaleId | undefined {
+  // Non-browser runs (node e2e booting the client tree) have no navigator.
+  if (typeof navigator === 'undefined') return undefined
+  for (const tag of [...navigator.languages, navigator.language]) {
+    const primary = tag.toLowerCase().split('-')[0]
+    const match = LOCALES.find(locale => locale.id === primary)
+    if (match) return match.id
+  }
+  return undefined
 }
 
 /** Persist the locale id; storage failures are non-fatal (preference resets next boot). */