The persons list search input used value={data.q || ''} bound directly to
server data, so every navigation completion would reset it to the URL value
mid-typing, dropping keystrokes just like issue #34 on the home page.
Apply the same focus-guard fix: introduce local `q` state, a `qFocused`
flag, and a guarded $effect that only syncs URL → state when the input is
not focused. Adds a regression test matching the home-page pattern.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
