Update Azure Functions guide to use OpenTelemetry (#15568)

## DESCRIBE YOUR PR
Resolves getsentry/sentry-dotnet#4726

See also:
- getsentry/sentry-dotnet#4763
- getsentry/sentry-dotnet#4786

## IS YOUR CHANGE URGENT?  

- [ ] Other deadline: Can be released any time before the version 6
release

## SLA

cc: @Flash0ver 

## PRE-MERGE CHECKLIST

- [ ] Checked Vercel preview for correctness, including links
- [ ] PR was reviewed and approved by any necessary SMEs (subject matter
experts)
- [ ] PR was reviewed and approved by a member of the [Sentry docs
team](https://github.com/orgs/getsentry/teams/docs)

Author: jamescrosswell

docs/platforms/dotnet/guides/azure-functions-worker/index.mdx

@@ -4,8 +4,7 @@ sdk: sentry.dotnet.azure.functions.worker
 description: "Learn about Sentry's .NET integration with Azure Functions."
 ---
 
-Sentry provides an integration with Azure Functions through the [Sentry.Azure.Functions.Worker NuGet package](https://www.nuget.org/packages/Sentry.Azure.Functions.Worker).
-All triggers are supported.
+Sentry provides an integration with Azure Functions through the [Sentry.Extensions.Logging](https://www.nuget.org/packages/Sentry.Extensions.Logging) and [Sentry.OpenTelemetry](https://www.nuget.org/packages/Sentry.OpenTelemetry) NuGet packages.
 
 ## Features
 
@@ -17,71 +16,76 @@ Select which Sentry features you'd like to install in addition to Error Monitori
 
 <OnboardingOptionButtons options={['error-monitoring', 'performance']}/>
 
-Add the Sentry dependency to your Azure Functions application:
+Add the Sentry dependencies to your Azure Functions application:
 
 ```shell {tabTitle:.NET Core CLI}
-dotnet add package Sentry.Azure.Functions.Worker -v {{@inject packages.version('sentry.dotnet.azure.functions.worker') }}
+dotnet add package Sentry.Extensions.Logging -v {{@inject packages.version('sentry.dotnet.extensions.logging') }}
+// ___PRODUCT_OPTION_START___ performance
+dotnet add package Sentry.OpenTelemetry -v {{@inject packages.version('sentry.dotnet.opentelemetry') }}
+dotnet add package OpenTelemetry
+dotnet add package OpenTelemetry.Extensions.Hosting
+dotnet add package OpenTelemetry.Instrumentation.Http
+
+// ___PRODUCT_OPTION_END___
 ```
 
 ```powershell {tabTitle:Package Manager}
-Install-Package Sentry.Azure.Functions.Worker -Version {{@inject packages.version('sentry.dotnet.azure.functions.worker') }}
+Install-Package Sentry.Extensions.Logging -Version {{@inject packages.version('sentry.dotnet.extensions.logging') }}
+// ___PRODUCT_OPTION_START___ performance
+Install-Package Sentry.OpenTelemetry -Version {{@inject packages.version('sentry.dotnet.opentelemetry') }}
+// ___PRODUCT_OPTION_END___
 ```
 
-This package extends [Sentry.Extensions.Logging](/platforms/dotnet/guides/extensions-logging/). This means that besides the Azure Functions related features, through this package you'll also get access to the `ILogger<T>` integration and also the features available in the main [Sentry](/platforms/dotnet/) SDK.
+The [Sentry.Extensions.Logging](/platforms/dotnet/guides/extensions-logging/) package also provides access to the `ILogger<T>` integration and the other core features available in the [Sentry](/platforms/dotnet/) SDK.
 
 ## Configure
 
-Sentry integration with Azure Functions is done by calling `.UseSentry()` and specifying the options, for example:
+The core features of Sentry are enabled by calling `AddSentry` when configuring logging.
 
-```csharp
-using Sentry.Azure.Functions.Worker;
-
-var builder = FunctionsApplication.CreateBuilder(args);
-
-builder.UseSentry(options =>
-{
-    options.Dsn = "___PUBLIC_DSN___";
-    // When configuring for the first time, to see what the SDK is doing:
-    options.Debug = true;
-    // Adds request URL and headers, IP and name for users, etc.
-    options.SendDefaultPii = true;
-    // ___PRODUCT_OPTION_START___ performance
-    // Set traces_sample_rate to 1.0 to capture 100% of transactions for performance monitoring.
-    // We recommend adjusting this value in production.
-    options.TracesSampleRate = 1.0;
-    // ___PRODUCT_OPTION_END___ performance
-});
-
-builder.Build().Run();
-```
-
-<Alert>
+<OnboardingOption optionId="performance">
+Performance tracing can be enabled by adding Sentry to the OpenTelemetry `TracerProviderBuilder` and then configuring Sentry itself to use OpenTelemetry.
+</OnboardingOption>
 
-If using the ASP.NET Core integration add `UseSentry` to the `ConfigureFunctionsWebApplication` call instead.
-
-</Alert>
+For example:
 
 ```csharp
-using Sentry.Azure.Functions.Worker;
+using Microsoft.Extensions.Hosting;
+using Microsoft.Extensions.Logging;
+using OpenTelemetry;
+// ___PRODUCT_OPTION_START___ performance
+using OpenTelemetry.Trace;
+// ___PRODUCT_OPTION_END___
+using Sentry.OpenTelemetry;
 
 var host = new HostBuilder()
-    .ConfigureFunctionsWorkerDefaults((host, builder) =>
+    .ConfigureFunctionsWorkerDefaults()
+// ___PRODUCT_OPTION_START___ performance
+    .ConfigureServices(services =>
+    {
+        services.AddOpenTelemetry().WithTracing(builder =>
+        {
+            builder
+                .AddSentry() // <-- Configure OpenTelemetry to send traces to Sentry
+                .AddHttpClientInstrumentation(); // From OpenTelemetry.Instrumentation.Http, instruments outgoing HTTP requests
+        });
+    })
+// ___PRODUCT_OPTION_END___
+    .ConfigureLogging(logging =>
     {
-        builder.UseSentry(host, options =>
+        logging.AddSentry(options =>
         {
             options.Dsn = "___PUBLIC_DSN___";
-            // When configuring for the first time, to see what the SDK is doing:
-            options.Debug = true;
-            // Adds request URL and headers, IP and name for users, etc.
-            options.SendDefaultPii = true;
             // ___PRODUCT_OPTION_START___ performance
-            // Set traces_sample_rate to 1.0 to capture 100% of transactions for performance monitoring.
-            // We recommend adjusting this value in production.
             options.TracesSampleRate = 1.0;
-            // ___PRODUCT_OPTION_END___ performance
+            options.UseOpenTelemetry(); // <-- Configure Sentry to use open telemetry
+            options.DisableSentryHttpMessageHandler = true; // So Sentry doesn't also create spans for outbound HTTP requests
+            // ___PRODUCT_OPTION_END___
+            options.Debug = true;
         });
     })
     .Build();
+
+
 await host.RunAsync();
 ```
 
@@ -93,4 +97,4 @@ This snippet includes an intentional error, so you can test that everything is w
 
 ## Samples
 
-- [Integration with Azure Functions](https://github.com/getsentry/sentry-dotnet/tree/main/src/Sentry.Azure.Functions.Worker) sample demonstrates Sentry with Azure Functions Isolated Worker SDK. (**C#**)
+- [Azure Functions Sample](https://github.com/getsentry/sentry-dotnet/blob/main/samples/Sentry.Samples.OpenTelemetry.AzureFunctions/) demonstrates Sentry with Azure Functions Isolated Worker SDK. (**C#**)