For issue #380. The dropdown now renders a dedicated search input at the
top, pre-filled with the text typed after @. This decouples the lookup
from the display text — the transcriber can edit the search field to
find a person whose stored name differs from what was typed.
The fetch wiring (onSearch callback) is consumed by PersonMentionEditor
in a follow-up commit; this commit only introduces the input UI and the
prop surface.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>