Use the correct JSON Schema mode when handling function schemas

[Viicos]

Change Summary

The mode property accounts for the json_schema_mode_override configuration value.

Related issue number

Checklist

• The pull request title is a good summary of the changes - it will be used in the changelog
• Unit tests for the changes exist
• Tests pass on CI
• Documentation reflects the changes where applicable
• My PR is ready to review, please add a comment including the phrase "please review" to assign reviewers

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[codspeed-hq]

CodSpeed Performance Report

Merging #11367 will not alter performance

_{Comparing json-schema-mode (8953aa9) with main (5e36892)}

Summary

✅ 45 untouched benchmarks

[github-actions]

Coverage report

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File	Statements	Missing	Coverage	Coverage (new stmts)	Lines missing
pydantic
json_schema.py
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