fix(web): screen readers don't repeat an old status when a dialog closes

NVDA reads a polite region's leftover text again when focus returns from a
dialog, so both thread announcers now clear their text a few seconds after
each announcement.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
4ecebd3019PR Batch Tester committed on 10/24/2026, 11:30:14 AMparent489ac64

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