Encourage web search usage in GPT handler

[jamesoncollins]

Motivation

• Reduce incorrect reliance on model internal knowledge by steering the Responses API to prefer web searches for factual, time-sensitive, or entity-specific queries.

Description

• Added a high-context WEB_SEARCH_TOOL, an allowed_tools WEB_SEARCH_TOOL_CHOICE, and expanded system guidance WEB_SEARCH_GUIDANCE to explicitly prefer web_search for facts and current information in handlers/gpt_handler.py.
• Implemented should_force_web_search(user_input) heuristic to detect prompts that should require a web search on the first model turn (URLs, time-sensitive terms, recent years, and key prefixes).
• Added build_response_create_kwargs(...) to centralize Responses API call construction and attach the tool_choice when force_web_search is true, and switched the handler to use this builder for initial and follow-up Responses calls.
• Surface a Web Search Forced flag in the diagnostic footer for visibility and adjusted the web_search tool spec to use search_context_size: "high".
• Added unit tests tests/test_gpt_handler.py covering the heuristic and kwargs builder.

Testing

• Ran python -m py_compile handlers/gpt_handler.py tests/test_gpt_handler.py, which succeeded.
• Ran python -m unittest tests/test_gpt_handler.py, which passed (all tests OK).
• Ran full test discovery OPENAI_API_KEY="" python3 -m unittest discover -s tests -p "test_*.py", which failed due to external network/proxy errors contacting third-party services (yt-dlp, yfinance, etc.); these failures are environment/network-related and not caused by the GPT handler changes.

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Codex Task