[http-client-java] Generate synchronous and asynchronous SSE operations

[XiaofeiCao]

Clear and concise description of the problem

The Java emitter does not generate complete public APIs and wiring for TypeSpec SSE operations.

Acceptance criteria

• Generates the approved synchronous consumption type and asynchronous Flux type.
• Connects operation methods to generated SSE decoding.
• Generates required imports, annotations, JavaDoc, and tests.
• Covers normal completion, early termination, errors, and cancellation.

Dependencies

• Parent: [FEATURE REQ] Full support for SSE Azure/azure-sdk-for-java#50264
• Synchronous API contract: [FEATURE REQ] Define the synchronous streaming API shape Azure/azure-sdk-for-java#50414
• Generated decoder: [http-client-java] Generate HTTP response-to-SSE decoding in service SDKs #11941

Checklist

• Follow our Code of Conduct
• Read the docs
• Checked for an existing duplicate

[github-actions]

🎯 Issue Triage

The Java client emitter needs to generate complete synchronous and asynchronous public APIs for TypeSpec SSE operations and connect them to the generated SSE decoder.
Category: Feature Request
Area: emitter:client:java

🔍 Analysis

This affects packages/http-client-java, specifically operation method generation, public synchronous consumption types, Reactor Flux return types, and the wiring between generated operations and SSE decoding. #11941 is a related dependency for the internal response-to-SSE decoder, not a duplicate; #11943 separately covers polymorphic event model generation. The requested behavior also requires generated imports, annotations, JavaDoc, and lifecycle tests for completion, early termination, errors, and cancellation.

📝 Suggested next steps

• Implement the synchronous and asynchronous operation signatures using the approved [FEATURE REQ] Define the synchronous streaming API shape Azure/azure-sdk-for-java#50414 contract.
• Wire operation response handling to the decoder generated by [http-client-java] Generate HTTP response-to-SSE decoding in service SDKs #11941.
• Add generation and runtime coverage for completion, early termination, errors, and cancellation.

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