fix(i18n): restore client workspace storage contract, reactive error banners, and demo gif

[mcocdaa]

Fixes Round-4 audit findings and CI client workspace contract:

• Remove direct localStorage usage from packages/client-core/src/http/apiError.ts and packages/client-ui/src/i18n/index.ts, routing locale persistence through configureLocalePreferences in apps/clients/web/src/adapters/browserThemePreferences.ts and syncing setApiErrorLocale.
• Re-translate active error banners reactively when toggling locale across views and composables.
• Localize agent.chat.bindingLabel in AgentChatSession.vue and AgentPreviewView.vue, and translate agent.preview.mobileKeybarHeading in zh.
• Re-record docs/assets/demo_termflow.gif (960x600, 49 frames, 27.93s duration, 1640ms keyframe holds).

[coderabbitai]

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