Env.set does not update process.env, breaking provider SDKs

[jerome-benoit]

After commit 90f39bf, Env.set only updates a shallow copy of process.env, not process.env itself. This breaks providers like sap-ai-core and amazon-bedrock whose SDKs read environment variables directly from process.env.

[github-actions]

This issue might be related to or could help explain several reported problems with provider SDKs. Please check these potentially related issues:

• fix(provider): Enable credential_process and default profile support for Amazon Bedrock #8559: Enable credential_process and default profile support for Amazon Bedrock - directly involves environment variable credential resolution
• Infinite installation loop of @aws-sdk/credential-providers on startup when AWS_BEARER_TOKEN_BEDROCK is set #6765: Infinite installation loop with AWS_BEARER_TOKEN_BEDROCK when set - AWS environment variable handling issue
• Slow startup when AWS_PROFILE is set #7614: Slow startup when AWS_PROFILE is set - environment variable processing affecting AWS SDK initialization
• Amazon bedrock support in Agent definition file #9607, Amazon Bedrock Model in Agents not work #9603, Amazon Bedrock model in agent file #9392: Multiple reports of Amazon Bedrock model not found errors in agent configuration - could be symptoms of this Env.set bug
• SAP AI Core - Connection parameters inconsistent #8737: SAP AI Core connection parameters inconsistent - affects the same sap-ai-core provider mentioned in this issue
• Excessive input token usage with Sonnet on AWS Bedrock #10066: Excessive input token usage with Sonnet on AWS Bedrock - could result from improper environment configuration

This bug could be the root cause of several of these reported issues if they involve environment variable-dependent provider SDKs.