feat(live): paginate catalog and search server-side (#49)

Load Live channels from a filtered SQLite cursor API, keep navigation and guide consumers working across pages, and retain the QA reproduction coverage.

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

server/routes/channels.js

@@ -1,6 +1,20 @@
 const express = require('express');
 const router = express.Router();
 const { getDb } = require('../db/sqlite');
+const { sources } = require('../db');
+const { parseQuery, getLiveCatalog } = require('../services/liveCatalog');
+
+router.get('/live-catalog', async (req, res) => {
+    try {
+        const options = parseQuery(req.query, req.user.id);
+        const result = getLiveCatalog(getDb(), await sources.getAll(), options);
+        res.json(result);
+    } catch (error) {
+        if (error.status === 400) return res.status(400).json({ error: error.message });
+        console.error('Error getting live catalog:', error);
+        res.status(500).json({ error: 'Failed to get live catalog' });
+    }
+});
 
 // Helper to map API item types to DB types and tables
 function mapItemType(apiType) {