feat(favicon): add favicon handling and serve functionality

* Implement favicon serving endpoint
* Add favicon.ico and favicon-source.png files

internal/app/app.go

@@ -113,6 +113,7 @@ func routes(logger *slog.Logger, cfg *config.Config, db *store.DB, provider ai.P
 
 	mcpHandler := mcpserver.New(cfg.MCP, toolSet)
 	mux.Handle(cfg.MCP.Path, auth.Middleware(cfg.Auth, keyring, logger)(mcpHandler))
+	mux.HandleFunc("/favicon.ico", serveFavicon)
 
 	mux.HandleFunc("/healthz", func(w http.ResponseWriter, r *http.Request) {
 		w.WriteHeader(http.StatusOK)

internal/app/favicon.go

@@ -0,0 +1,24 @@
+package app
+
+import (
+	_ "embed"
+	"net/http"
+)
+
+var (
+	//go:embed static/favicon.ico
+	faviconICO []byte
+)
+
+func serveFavicon(w http.ResponseWriter, r *http.Request) {
+	w.Header().Set("Content-Type", "image/x-icon")
+	w.Header().Set("Cache-Control", "public, max-age=31536000, immutable")
+
+	if r.Method == http.MethodHead {
+		w.WriteHeader(http.StatusOK)
+		return
+	}
+
+	w.WriteHeader(http.StatusOK)
+	_, _ = w.Write(faviconICO)
+}