feat(sort): persist sort order in URL as ?sort= param

Sort was local state, lost on navigation. Now reads from
searchParams.get('sort') and pushes to URL on change.
'default' removes the param to keep URLs clean.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

nextjs-app/components/HomeView.tsx

@@ -6,7 +6,7 @@
 'use client';
 
 import { useState, useEffect, useRef } from 'react';
-import { useSearchParams } from 'next/navigation';
+import { useSearchParams, useRouter, usePathname } from 'next/navigation';
 import { FilterBar } from './FilterBar';
 import { SchoolRow } from './SchoolRow';
 import { SecondarySchoolRow } from './SecondarySchoolRow';
@@ -26,10 +26,12 @@ interface HomeViewProps {
 
 export function HomeView({ initialSchools, filters, totalSchools }: HomeViewProps) {
   const searchParams = useSearchParams();
+  const router = useRouter();
+  const pathname = usePathname();
   const { addSchool, removeSchool, selectedSchools } = useComparisonContext();
   const [resultsView, setResultsView] = useState<'list' | 'map'>('list');
   const [selectedMapSchool, setSelectedMapSchool] = useState<School | null>(null);
-  const [sortOrder, setSortOrder] = useState<string>('default');
+  const sortOrder = searchParams.get('sort') || 'default';
   const [allSchools, setAllSchools] = useState<School[]>(initialSchools.schools);
   const [currentPage, setCurrentPage] = useState(initialSchools.page);
   const [hasMore, setHasMore] = useState(initialSchools.total_pages > 1);
@@ -193,7 +195,19 @@ export function HomeView({ initialSchools, filters, totalSchools }: HomeViewProp
                 </div>
               )}
               {resultsView === 'list' && (
-                <select value={sortOrder} onChange={e => setSortOrder(e.target.value)} className={styles.sortSelect}>
+                <select
+                  value={sortOrder}
+                  onChange={e => {
+                    const params = new URLSearchParams(searchParams);
+                    if (e.target.value === 'default') {
+                      params.delete('sort');
+                    } else {
+                      params.set('sort', e.target.value);
+                    }
+                    router.push(`${pathname}?${params.toString()}`);
+                  }}
+                  className={styles.sortSelect}
+                >
                   <option value="default">Sort: Relevance</option>
                   {!isSecondaryView && <option value="rwm_desc">Highest R, W &amp; M %</option>}
                   {!isSecondaryView && <option value="rwm_asc">Lowest R, W &amp; M %</option>}