fix(websearch): remove 'deep' option from search type and update descriptions

[Danztee]

Issue for this PR

Closes #21044

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

Fixes a mismatch in the websearch tool config.

We were advertising deep as a valid search type, but the Exa backend only accepts auto and fast. So if a user passed deep, it failed at runtime with a validation error from the backend.

This change removes deep from the tool schema and updates the tool description text to match what the backend actually supports. That way we don’t present an option that can never work.

How did you verify your code works?

• Reproduced the issue first using type: "deep" and confirmed backend rejection
• Updated schema/docs to only allow auto and fast.
• Ran bun turbo typecheck.

Screenshots / recordings

If this is a UI change, please include a screenshot or recording.

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

[Danztee]

Hi @adamdotdevin can you check this pls??