Forward visitor request when lazily caching Examples

[abidlabs]

Describe the bug

When gr.Examples uses lazy caching, the first click executes the example function through an internal Blocks.process_api(..., request=None) call. As a result, the visitor request context is discarded. In a Space or Pod that calls a downstream ZeroGPU Space with gradio_client, the downstream call therefore cannot forward the visitor's X-IP-Token and is charged as visitor-less Space GPU usage.

Expected behavior

The first visitor who clicks a lazily cached example should provide the request context used to compute that cache entry, so downstream ZeroGPU calls receive that visitor's X-IP-Token. Subsequent clicks should continue to use the shared cached result without rerunning the function. Eager startup caching can remain visitor-less because no request exists.

Reproduction

1. Build a Gradio app with gr.Examples(..., cache_examples=True, cache_mode="lazy").
2. In the example function, inspect gradio.context.LocalContext.request or create a gradio_client.Client for a downstream ZeroGPU Space.
3. Click an example while sending an X-IP-Token header.
4. Observe that the example function runs with no request and the token is not forwarded.

Additional context

Pod/Space GPU usage without X-IP-Token is being deprecated, so lazy example execution needs to be attributed to the clicking visitor.