feat(cast): add server-managed Google Cast playback (#34)

Add server-side Google Cast discovery and sessions, signed cast media URLs, browser device picker integration, and deployment documentation.

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

server/index.js

@@ -182,6 +182,7 @@ app.use('/api/settings', require('./routes/settings'));
 app.use('/api/history', require('./routes/history'));
 app.use('/api/laya', require('./routes/laya'));
 app.use('/api/live', require('./routes/live'));
+app.use('/api/cast', require('./routes/cast'));
 
 // Version endpoint
 app.get('/api/version', (req, res) => {