Fix Azure deployment model request body

[fengjikui]

Fixes #2892.

Summary

• omit model from Azure deployment-based request bodies after using it to route /deployments/{deployment}
• preserve the caller-provided JSON body by copying request options before removing model
• add sync/async Azure regression coverage for image generation deployments whose names differ from model IDs

Validation

• env -u HTTP_PROXY -u HTTPS_PROXY -u ALL_PROXY -u http_proxy -u https_proxy -u all_proxy uv run --with pytest --with pytest-xdist --with pytest-asyncio --with respx --with httpx --with rich pytest tests/lib/test_azure.py -q
• env -u HTTP_PROXY -u HTTPS_PROXY -u ALL_PROXY -u http_proxy -u https_proxy -u all_proxy uv run --with ruff ruff check src/openai/lib/azure.py tests/lib/test_azure.py
• env -u HTTP_PROXY -u HTTPS_PROXY -u ALL_PROXY -u http_proxy -u https_proxy -u all_proxy uv run python -m py_compile src/openai/lib/azure.py tests/lib/test_azure.py