API Gateway not forwarding real path to Lambda

I have a Lambda (Go) behind an HTTP API Gateway. Route /webhook is set correctly (payload format 2.0, not $default), but every request to /webhook still triggers my root / handler, im not getting the webhook handler for some reason.

func main() {
    mux := http.NewServeMux()

    mux.HandleFunc("/", func(w http.ResponseWriter, r *http.Request) {
        fmt.Fprint(w, "hello world")
    })

    mux.HandleFunc("/health", func(w http.ResponseWriter, r *http.Request) {
        w.WriteHeader(http.StatusOK)
    })

    mux.HandleFunc("/webhook", webhookHandler)

    adapter := httpadapter.NewV2(mux)
    lambda.Start(adapter.ProxyWithContext)
}