[release] Prepare release coreunstable-1.13.1-beta.1 (#6599)

Co-authored-by: opentelemetrybot <[email protected]>
Co-authored-by: Piotr Kiełkowicz <[email protected]>

Author: 3 people

src/OpenTelemetry.Exporter.Prometheus.AspNetCore/CHANGELOG.md

@@ -13,6 +13,10 @@ Notes](../../RELEASENOTES.md).
   `Microsoft.Extensions.Logging.Configuration` NuGet packages.
   ([#6327](https://github.com/open-telemetry/opentelemetry-dotnet/pull/6327))
 
+## 1.13.1-beta.1
+
+Released 2025-Oct-10
+
 * Updated OpenTelemetry core component version(s) to `1.13.1`.
   ([#6598](https://github.com/open-telemetry/opentelemetry-dotnet/pull/6598))
 

src/OpenTelemetry.Exporter.Prometheus.HttpListener/CHANGELOG.md

@@ -13,6 +13,10 @@ Notes](../../RELEASENOTES.md).
   `Microsoft.Extensions.Logging.Configuration` NuGet packages.
   ([#6327](https://github.com/open-telemetry/opentelemetry-dotnet/pull/6327))
 
+## 1.13.1-beta.1
+
+Released 2025-Oct-10
+
 * Updated OpenTelemetry core component version(s) to `1.13.1`.
   ([#6598](https://github.com/open-telemetry/opentelemetry-dotnet/pull/6598))
 

src/OpenTelemetry.Shims.OpenTracing/CHANGELOG.md

@@ -6,6 +6,10 @@ Notes](../../RELEASENOTES.md).
 
 ## Unreleased
 
+## 1.13.1-beta.1
+
+Released 2025-Oct-10
+
 * Updated OpenTelemetry core component version(s) to `1.13.1`.
   ([#6598](https://github.com/open-telemetry/opentelemetry-dotnet/pull/6598))