openai: embeddings path never honors OTEL_INSTRUMENTATION_GENAI_CAPTURE_MESSAGE_CONTENT

What I observed

The OpenAI embeddings example documents message-content capture, but the embeddings code path never consults the content-capture setting.

In instrumentation/opentelemetry-instrumentation-genai-openai/src/opentelemetry/instrumentation/genai/openai/patch.py, the chat paths read the setting and thread it through:

• chat_completions_create — capture_content = handler.should_capture_content() (line 65), passed to _create_chat_invocation(...) and _set_response_properties(...)
• the async variant does the same at line 96

The embeddings path does not:

• embeddings_create (line 124) calls _create_embedding_invocation(handler, kwargs, instance) with no capture_content argument
• _create_embedding_invocation (lines 34-58) records only request_model, server_address, server_port, dimension_count, and encoding_formats. The embedding input is never recorded on the span or emitted as an event.

Meanwhile instrumentation/opentelemetry-instrumentation-genai-openai/examples/embeddings/README.rst tells the user that setting OTEL_INSTRUMENTATION_GENAI_CAPTURE_MESSAGE_CONTENT "configures OpenAI instrumentation to capture content on events", and the accompanying .env sets it. Following that example produces no content for embeddings regardless of the value.

Observed on main at 15d92a7.

Question

Is this intentional — embedding inputs are deliberately never captured, in which case the embeddings example's documentation is the thing that is wrong — or is it a gap in the embeddings path?

I am happy to send a PR either way once you tell me which direction you prefer:

1. Adjust the embeddings example documentation so it does not advertise content capture, or
2. Thread capture_content through the embeddings path so the setting is honored.

I did not want to guess at the intended semantics for embedding inputs, since capturing them has different privacy characteristics from chat prompts.

Start in instrumentation/opentelemetry-instrumentation-genai-openai/src/opentelemetry/instrumentation/genai/openai/patch.py, comparing embeddings_create and _create_embedding_invocation with the chat paths' content-capture handling. Review instrumentation/opentelemetry-instrumentation-genai-openai/examples/embeddings/README.rst and its .env to determine which behavior is intended. Done means the implementation and example documentation consistently describe and honor the chosen content-capture behavior.