Add custom headers for OpenAI-compatible providers

[chindris-mihai-alexandru]

Summary

This refreshes the earlier custom-header work from #42817 and #45673 with a smaller, settings-first implementation.

It adds custom_headers support to language_models.openai_compatible, threads those headers through both /chat/completions and /responses, and documents the setting in the provider docs.

While testing custom OpenAI-compatible gateways, I also ran into streaming responses that emit data: null keepalive chunks, so this PR skips those chunks instead of failing deserialization.

Testing

• cargo test -p open_ai -q
• cargo check -p zed

Release Notes:

• Improved OpenAI-compatible providers to support custom HTTP headers and ignore null SSE keepalive events.

[Copilot]

Pull request overview

Adds first-class support for user-configured custom HTTP headers for OpenAI-compatible providers, and improves streaming robustness by ignoring data: null SSE keepalive events.

Changes:

• Add custom_headers to language_models.openai_compatible settings and plumb them through OpenAI /chat/completions and /responses requests.
• Ignore data: null SSE chunks during streaming for both Chat Completions and Responses APIs.
• Update provider documentation and update call sites for the new streaming function signatures.

Reviewed changes

Copilot reviewed 12 out of 12 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
docs/src/ai/llm-providers.md	Documents custom_headers for OpenAI-compatible gateways.
crates/settings_content/src/language_model.rs	Adds custom_headers to OpenAI-compatible settings schema.
crates/open_ai/src/open_ai.rs	Threads custom headers into chat completions streaming; ignores null SSE events; adds unit tests.
crates/open_ai/src/responses.rs	Threads custom headers into responses streaming; ignores null SSE events; adds unit tests.
crates/language_models/src/settings.rs	Maps settings custom_headers into runtime provider settings.
crates/language_models/src/provider/open_ai_compatible.rs	Passes configured custom headers into OpenAI request helpers.
crates/language_models/src/provider/open_ai.rs	Updates OpenAI provider calls for new function signature (passes None).
crates/language_models/src/provider/x_ai.rs	Updates call for new function signature (passes None).
crates/language_models/src/provider/vercel.rs	Updates call for new function signature (passes None).
crates/language_models/src/provider/vercel_ai_gateway.rs	Updates call for new function signature (passes None).
crates/language_models/src/provider/opencode.rs	Updates calls for new function signature (passes None).
crates/agent_ui/src/agent_configuration/add_llm_provider_modal.rs	Ensures new providers written to settings include custom_headers field.

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[bennetbo]

Thanks for working on this. Closing in favour of #55246