feat: Integrate OpenAI Responses API to enable GPT-5 features

[ferenci84]

Description

OpenAI Responses API integration to enable GPT‑5 features

This PR adds first-class support for the OpenAI Responses API (streaming and non‑streaming) and routes supported models (o‑series, GPT‑5) through it. The Responses API is required to fully use GPT‑5 features like native reasoning, structured output items, and robust tool calling.

What changed

• Responses API request/response handling for both streaming and non‑streaming flows
• Support for reasoning items and structured outputs; tool calls with proper argument streaming
• Persisted provider metadata to correctly pair reasoning and output items across turns
• Type‑safe request bodies and simplified event handling
• Kept Chat Completions for legacy/non‑supported models (backward compatible)

Impact

• Unlocks GPT‑5 capabilities end‑to‑end in Continue
• More reliable tool calling and reasoning visibility
• Minimal UI/state updates to surface new metadata and avoid duplicate output

No breaking changes for existing non‑o‑series models.

Please note that the changes was made on top of other PR changes #7073 as it contained changes required by this feature.

Related issues:
#5730
#7618

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Checklist

• I've read the contributing guide
• The relevant docs, if any, have been updated or created
• The relevant tests, if any, have been updated or created

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Tests

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Summary by cubic

Integrates the OpenAI Responses API to unlock GPT‑5 and o‑series features (reasoning, structured outputs, stronger tool calls) while keeping Chat Completions for legacy models. Improves streaming, logging, and UI/state to surface reasoning and tool metadata reliably.

• New Features

  • Add OpenAI Responses API support (streaming and non‑streaming) and route GPT‑5/o‑series models through it.
  • Preserve and emit reasoning content and reasoning_details; handle Claude signatures safely; store per‑message metadata.
  • Improve tool calling with function call items and argument streaming; pair tool outputs via stable output item IDs.
  • Type‑safe conversions: map Responses input/output to internal messages (toResponsesInput/fromResponsesChunk) including thinking blocks.
  • Provider capability flags for reasoning fields; enabled for Deepseek and OpenRouter.
  • Backward compatible: non‑supported models still use Chat Completions.

• Refactors

  • Faster streaming: accumulate chunks in arrays and join once; unified chunk processing and usage tracking.
  • Better logging, including optional citation messages at the end of streams.
  • Clearer error handling across providers (404/401 and missing /v1 guidance).
  • UI/state updates: action visibility tweaks in StepContainer; merge reasoning_details across chunks and track responsesOutputItemId in session state.

[RomneyDa]

@sestinj bumping this for gpt 5 codex!

[RomneyDa]

@ferenci84 just double checking, this PR includes everything from #7073? Seems like besides the merge commits I pushed to #7073 it's the same, could I just close that one and merge this one or am I missing some nuance there?

[Patrick-Erichsen]

llm-index-merge-resolution.patch

@ferenci84 mind taking a look at this patch to handle the merge conflict? If it's good let's apply it, once we get the conflict resolved I think this is good to merge 👍