fix: decouple LiteLLM web search from Codex search tool

[AviBackToBlack]

Summary

Follow up the merged foreign web-search compatibility contract from #22 with the intentionally small production fix it identified.

This PR:

• stops mapping LiteLLM supports_web_search=false to Codex supports_search_tool=false for exact templates
• stops treating supports_web_search overrides as provenance/ownership for exact supports_search_tool
• keeps foreign supports_search_tool=false as a conservative tool-search/deferred-discovery decision, not a hosted-web-search suppression guarantee
• keeps LiteLLM/override supports_web_search visible as capability evidence in explain
• adds regressions for raw exact evidence, exact overrides, and foreign override provenance
• aligns the older model-group aggregation design text with the source-backed web-search contract

No foreign hosted-web-search enablement is added. Provider/runtime hosted-search behavior remains deferred under docs/foreign-web-search.md.

Refs #5

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[devin-ai-integration]

✅ Devin Review: No Issues Found

Devin Review analyzed this PR and found no bugs or issues to report.