Update dependency Azure.Core to 1.51.1

[renovate]

This PR contains the following updates:

Package	Change	Age	Confidence
Azure.Core (source)	1.50.0 → 1.51.1

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Release Notes

Azure/azure-sdk-for-net (Azure.Core)

v1.51.1

Compare Source

1.51.1 (2026-02-04)

Features Added

• Update the APIs for Microsoft.Extensions.Configuration and Microsoft.Extensions.DependencyInjection to enable Azure.Identity use cases.
• Updated BCL dependencies to 10.x.

v1.51.0

Compare Source

1.51.0 (2026-01-29)

Features Added

• Added core support for Microsoft.Extensions.Configuration and Microsoft.Extensions.DependencyInjection.
• Implements support for client certificate rotation in the Azure.Core transport layer to enable dynamic token binding scenarios. The changes allow transport instances to be updated with new client certificate configurations at runtime without requiring full pipeline reconstruction.

Bugs Fixed

• Fixed NullReferenceException when calling GetHashCode() on default(AzureLocation).

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