[release] Prepare release coreunstable-1.13.0-beta.1 (#6553)

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

Author: otelbot-dotnet[bot]

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

@@ -7,6 +7,10 @@ Notes](../../RELEASENOTES.md).
 
 ## Unreleased
 
+## 1.13.0-beta.1
+
+Released 2025-Oct-01
+
 * Updated OpenTelemetry core component version(s) to `1.13.0`.
   ([#6552](https://github.com/open-telemetry/opentelemetry-dotnet/pull/6552))
 

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

@@ -7,6 +7,10 @@ Notes](../../RELEASENOTES.md).
 
 ## Unreleased
 
+## 1.13.0-beta.1
+
+Released 2025-Oct-01
+
 * Updated OpenTelemetry core component version(s) to `1.13.0`.
   ([#6552](https://github.com/open-telemetry/opentelemetry-dotnet/pull/6552))
 

src/OpenTelemetry.Shims.OpenTracing/CHANGELOG.md

@@ -6,6 +6,10 @@ Notes](../../RELEASENOTES.md).
 
 ## Unreleased
 
+## 1.13.0-beta.1
+
+Released 2025-Oct-01
+
 * Updated OpenTelemetry core component version(s) to `1.13.0`.
   ([#6552](https://github.com/open-telemetry/opentelemetry-dotnet/pull/6552))