feat: new tool - prediction websearch

[LOCKhart07]

Proposed changes

Introduce a new tool prediction-websearch

Features:

• Uses openai websearch api directly instead of relying on google search
• Uses structured output calling from openai instead of parsing through the output manually

Notes:

• Has extremely high token costs relative to existing tools
• Only supports openai models for now.
• Want to add support for gpt-5 because it costs less to use websearch api with gpt5 https://platform.openai.com/docs/pricing#built-in-tools
• This will probably get better roi with higher bet sizes because of it's high token cost

Fixes

Ideally should have higher accuracy

Types of changes

• Non-breaking fix (non-breaking change which fixes an issue)
• Breaking fix (breaking change which fixes an issue)
• Non-breaking feature (non-breaking change which adds functionality)
• Breaking feature (breaking change which adds functionality)
• Refactor (non-breaking change which changes implementation)
• Messy (mixture of the above - requires explanation!)

Checklist

• I have read the CONTRIBUTING doc
• I am making a pull request against the main branch (left side). Also you should start your branch off our main.
• Lint and unit tests pass locally with my changes
• I have added tests that prove my fix is effective or that my feature works

Further comments

Apart from the general stuff, As part of review, I'm looking for suggestions on:

• Tool name
• A way to test this tool against pre existing tools.
  • My current plan is to take some 30 or so markets that will close in a day or two.
  • Run all existing tools plus this one against these markets and then check results after the markets close
• If this approach could work even with the high token costs

Comparison with Existing Approaches

Web Search Tier	Multiplier vs. 1k GPT-4.1 Tokens
GPT-4.1 / GPT-4o	~3.1× more expensive
GPT-5 / o-series	~1.25× more expensive