refactor: split nats-chatroom into modules with profile, layout, and auth

Extract chat, profile, types, and user data into separate files.
Embed CSS via go:embed. Add a layout with nav, session-based profile
persistence, and a middleware guard that redirects to /profile when
no identity is set.

internal/examples/nats-chatroom/userdata.go

@@ -0,0 +1,22 @@
+package main
+
+import "math/rand"
+
+var quoteIdx = rand.Intn(len(devQuotes))
+var devQuotes = []string{
+	"Just use NATS.",
+	"Pub/sub all the things!",
+	"Messages are the new API.",
+	"JetStream for durability.",
+	"No more polling.",
+	"Event-driven architecture FTW.",
+	"Decouple everything.",
+	"NATS is fast.",
+	"Subjects are like topics.",
+	"Request-reply is cool.",
+}
+
+func randomDevQuote() string {
+	quoteIdx = (quoteIdx + 1) % len(devQuotes)
+	return devQuotes[quoteIdx]
+}