docs(js): Use client from init method in js snippets (#10460)

Author: chargome

platform-includes/performance/automatic-instrumentation-custom-routing/javascript.mdx

@@ -5,7 +5,7 @@ By default, the `browserTracingIntegration()` will create a `pageload` span for
 To make sure that spans are created correctly for a custom routing setup, you'll need to opt out of the default span creation by setting `instrumentNavigation: false` and `instrumentPageLoad: false` in the `browserTracingIntegration()` options. You can then manually create spans like this:
 
 ```javascript
-Sentry.init({
+const client = Sentry.init({
   integrations: [
     Sentry.browserTracingIntegration({
       // disable automatic span creation
@@ -15,8 +15,6 @@ Sentry.init({
   ],
 });
 
-const client = Sentry.getClient()
-
 // We start the pageload span as early as possible!
 let pageLoadSpan = Sentry.startBrowserTracingPageLoadSpan(client, {
   name: window.location.pathname,

platform-includes/performance/opentelemetry-setup/javascript.node.mdx

@@ -33,15 +33,14 @@ function setupSentry() {
   setupGlobalHub();
 
   // Make sure to call `Sentry.init` BEFORE initializing the OpenTelemetry SDK
-  Sentry.init({
+  const client = Sentry.init({
     dsn: "___PUBLIC_DSN___",
     tracesSampleRate: 1.0,
     // set the instrumenter to use OpenTelemetry instead of Sentry
     instrumenter: "otel",
     // ...
   });
 
-  const client = getClient();
   setupEventContextTrace(client);
 
   // You can wrap whatever local storage context manager you want to use