Forward visitor requests when lazily caching examples - #13822

Description

Lazy gr.Examples caching ran the user function through an internal process_api call with request=None, so downstream ZeroGPU clients could not forward the clicking visitor's X-IP-Token. This passes the click request through the lazy cache path while leaving eager startup caching visitor-less. A regression test covers the API request header reaching the example function.

Closes: #13821

AI Disclosure

• I used AI to investigate the request flow, draft the scoped implementation and regression test, and prepare this PR. I self-reviewed every changed line.
• I did not use AI

Testing and Formatting Your Code

• PYTHONPATH=client/python:. MPLCONFIGDIR=/tmp/gradio-13821-mpl pytest -q test/test_helpers.py::TestProcessExamples::test_lazy_cache_examples_preserves_request
• python3 -m ruff check gradio/helpers.py test/test_helpers.py
• python3 -m ruff format --check gradio/helpers.py test/test_helpers.py
• ty check --python /Library/Frameworks/Python.framework/Versions/3.14/bin/python3 --extra-search-path client/python gradio/helpers.py test/test_helpers.py

The repository-wide formatting wrapper could not use its python command in this shell, so the equivalent scoped Ruff commands above were run directly. The full launch-based helper class also requires built frontend assets; the new in-process regression passes and CI will run the configured full suite.

Minimal reproduction

import gradio as gr


def show_visitor(value: str, request: gr.Request) -> str:
    token = request.headers.get("x-ip-token") if request else None
    return f"{value}: {token or 'missing'}"


with gr.Blocks() as demo:
    prompt = gr.Textbox(label="Prompt")
    result = gr.Textbox(label="X-IP-Token seen by the example function")
    gr.Examples(
        examples=["mountain landscape", "city skyline"],
        inputs=prompt,
        outputs=result,
        fn=show_visitor,
        cache_examples=True,
        cache_mode="lazy",
    )

demo.launch()

The demo file is intentionally untracked and was not committed.