Host-page voice menu is slow to reflect a voice chosen in the settings catalog

[rosscado]

Founder tasting feedback on Patch A (#470), 2026-07-02.

Repro: with claude.ai open, pick a voice in the settings Voices catalog (e.g. switch Cassidy → Lucy). TTS switches immediately — the next utterance is in Lucy's voice — but the host page's voice menu button still says "Cassidy" for a noticeable interval before it eventually catches up.

So the preference write propagates to the speech path promptly, but nothing pushes the change into ClaudeVoiceMenu's button label/checkmarks; it presumably only refreshes on the next menu open / repopulate cycle.

Work:

• Trace how a settings-page setVoice reaches the content script (chrome.storage.onChanged → EventBus?) and have the voice selectors subscribe: on a voice-preference change, update the selector synchronously (updateSelectedVoice on Claude; selected-button marking on Pi) without waiting for a repopulate.
• Same-tab selection already updates immediately; keep that path intact.
• Mind the open-menu guard from feat(voices): capped in-host voice menus, HD tier signalling, settings voice catalog (Patch A) #470: never tear down a menu the user has open.

Part of the #471 feedback batch.