fix(persons): prevent stale navigation from clobbering focused search input

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>

frontend/src/routes/persons/+page.svelte

@@ -1,16 +1,24 @@
 <script lang="ts">
 import { goto } from '$app/navigation';
+import { untrack } from 'svelte';
 import { m } from '$lib/paraglide/messages.js';
 
 let { data } = $props();
 
+let q = $state(untrack(() => data.q || ''));
+let qFocused = $state(false);
+
+// Sync URL → local state after navigation, but not while the user is typing.
+$effect(() => {
+	if (!qFocused) q = data.q || '';
+});
+
 let searchTimeout: ReturnType<typeof setTimeout>;
 
-function handleSearch(e: Event) {
-	const value = (e.target as HTMLInputElement).value;
+function handleSearch() {
 	clearTimeout(searchTimeout);
 	searchTimeout = setTimeout(() => {
-		goto(`/persons?q=${value}`, { keepFocus: true });
+		goto(`/persons?q=${q}`, { keepFocus: true });
 	}, 300);
 }
 </script>
@@ -49,8 +57,10 @@ function handleSearch(e: Event) {
 					id="search"
 					type="text"
 					placeholder={m.persons_search_placeholder()}
-					value={data.q || ''}
+					bind:value={q}
 					oninput={handleSearch}
+					onfocus={() => (qFocused = true)}
+					onblur={() => (qFocused = false)}
 					class="block w-full rounded-sm border border-gray-300 bg-white py-2.5 pr-10 pl-4 font-sans text-sm text-brand-navy placeholder-gray-400 shadow-sm focus:border-brand-navy focus:ring-1 focus:ring-brand-navy focus:outline-none"
 				/>
 				<div