fix(live): index category lookups for catalog search (#49)

Avoid repeated category scans while filtering the paginated Live catalog, and keep the search timing and query-plan reproductions in the regression suite.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

test/live-catalog-initial-load.test.js

@@ -77,6 +77,18 @@ async function requestAllPages(base, cookie, query = {}) {
     return items;
 }
 
+test('application startup creates the composite category lookup index', async t => {
+    const app = await startApp(t);
+    const response = await request(app.base, app.cookie);
+    assert.equal(response.status, 200);
+    const db = new Database(path.join(app.dir, 'content.db'), { fileMustExist: true });
+    t.after(() => db.close());
+    const index = db.prepare(`SELECT sql FROM sqlite_master
+        WHERE type='index' AND name='idx_categories_source_type_category'`).get();
+    assert.ok(index, 'startup schema should create idx_categories_source_type_category');
+    assert.match(index.sql, /\(source_id,\s*type,\s*category_id\)/i);
+});
+
 function seedCatalog(dir, userId) {
     const db = new Database(path.join(dir, 'content.db'));
     const insertCategory = db.prepare(`