fix(core): use dedicated types for responsesapi web search tool config

[owenlin0]

This changes the web_search tool spec in codex-core to use dedicated Responses-API payload structs instead of shared config types and custom serializers.

Previously, ToolSpec::WebSearch stored WebSearchFilters and WebSearchUserLocation directly and relied on hand-written serializers to shape the outgoing JSON. This worked, but it mixed config/schema types with the OpenAI Responses payload contract and created an easy place for drift if those shared types changed later.

Why

This keeps the boundary clearer:

• app-server/config/schema types stay focused on config
• Responses tool payload types stay focused on the OpenAI wire format

It also makes the serialization behavior obvious from the structs themselves, instead of hiding it in custom serializer functions.

[owenlin0]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Nice work!

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