feat: add SSE keepalive and liveness tracking for resilient connections

Add 30s keepalive pings to prevent proxy/CDN idle timeouts from killing
SSE connections silently. Track lastSeenAt on each SSE connect attempt
so Datastar's retry signals keep contexts alive through the reaper.

context.go

@@ -42,6 +42,7 @@ type Context struct {
 	createdAt           time.Time
 	sseConnected        atomic.Bool
 	sseDisconnectedAt   atomic.Pointer[time.Time]
+	lastSeenAt          atomic.Pointer[time.Time]
 	suspended           atomic.Bool
 }