fix(dedupe): make edge contradiction reasoning explicit

[Whxuan0701]

Closes #1666

Summary

• Add a reasoning field to the EdgeDuplicate structured response before the final index arrays.
• Require prompt reasoning to cite continuous fact indices before returning duplicate/contradiction lists.
• Keep the field optional for backward compatibility with providers that omit it.

Design

Structured-output field order gives non-reasoning small models an explicit place to analyze facts before emitting indices. The existing duplicate and contradiction arrays remain unchanged, so downstream validation and invalidation behavior is preserved.

Tests

• uv run --with pytest --with pytest-asyncio pytest --confcutdir=tests/prompts tests/prompts/test_dedupe_edges.py tests/utils/maintenance/test_edge_operations.py -q (11 passed)
• Ruff check and format check on changed files.

Compatibility/Risks

Additive response-model field with an empty default. This improves the prompt/schema contract but cannot guarantee model accuracy for every provider or model. No external LLM calls were required.

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[linhongyu510]

The new reasoning field is optional (default=""), so the raw Pydantic schema does not include it in required. That undercuts the mechanism this PR and #1666 rely on: OpenAIGenericClient and AnthropicClient pass model_json_schema() directly, and Gemini likewise consumes the model/schema, so those providers may legally emit the two arrays without first generating reasoning. The issue’s measured variant used Field(...); the new test checks only declaration order and therefore misses this. Please make reasoning required and assert that reasoning is present in EdgeDuplicate.model_json_schema()["required"] (ideally also cover a provider-facing schema path). I reproduced the current schema on 8f559931: required == ["duplicate_facts", "contradicted_facts"], while the focused 11 tests still pass. Also please remove the stray literal apostrophes embedded at the ends of the new prompt lines (reasoning field. ', reasoning ', the '); the current test only checks substrings and does not catch the malformed prompt text.