feat: Update snippet to use logger.X (#13657)

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Based on feedback from slack after merging in
#13603

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Author: AbhiPrasad

includes/logs/javascript-usage.mdx

@@ -2,30 +2,34 @@ Once the feature is enabled on the SDK and the SDK is initialized, you can send
 
 The `Sentry.logger` namespace exposes six methods that you can use to log messages at different log levels: `trace`, `debug`, `info`, `warn`, `error`, and `fatal`.
 
-Aside from the primary logging methods, we've provided a format text function, `fmt`, that you can use to add insert properties into to your log entries.
+Aside from the primary logging methods, we've provided a format text function, `Sentry.logger.fmt`, that you can use to add insert properties into to your log entries.
+
 These properties will be sent to Sentry, and can be searched from within the Logs UI, and even added to the Logs views as a dedicated column.
 
 ```js
-const { info, warn, fmt } = Sentry.logger;
+const { logger } = Sentry;
 
-error(fmt`Uh on, something broke, here's the error: '${error}'`);
-info(fmt`User '${user.username}' added item '${product.name}' to cart.`);
+logger.error(logger.fmt`Uh on, something broke, here's the error: '${error}'`);
+logger.info(logger.fmt`'${user.username}' added '${product.name}' to cart.`);
 ```
 
 You can also pass additional attributes directly to the logging functions, avoiding the need to use the `fmt` function.
 
 ```js
-const { trace, debug, info, warn, error, fatal } = Sentry.logger;
+const { logger } = Sentry;
 
-trace("Starting database connection", { database: "users" });
-debug("Cache miss for user", { userId: 123 });
-info("Updated profile", { profileId: 345 });
-warn("Rate limit reached for endpoint", {
+logger.trace("Starting database connection", { database: "users" });
+logger.debug("Cache miss for user", { userId: 123 });
+logger.info("Updated profile", { profileId: 345 });
+logger.warn("Rate limit reached for endpoint", {
   endpoint: "/api/results/",
   isEnterprise: false,
 });
-error("Failed to process payment", { orderId: "order_123", amount: 99.99 });
-fatal("Database connection pool exhausted", {
+logger.error("Failed to process payment", {
+  orderId: "order_123",
+  amount: 99.99,
+});
+logger.fatal("Database connection pool exhausted", {
   database: "users",
   activeConnections: 100,
 });