Update Factory setup guide for settings.json

[TinyFrontier]

Summary

• update the Factory CLI example from the legacy ~/.factory/config.json format to ~/.factory/settings.json
• convert the custom model configuration from snake_case to the current camelCase field names
• document that the legacy format remains supported and that settings.json takes precedence
• add a direct link to Factory's current BYOK configuration reference

Why

Factory's current BYOK documentation uses settings.json and the customModels, displayName, baseUrl, and apiKey field names. The existing guide still presents the backward-compatible legacy format as the primary setup path.

This update lets new users copy the current recommended configuration while retaining migration context for existing users. It does not change model IDs, endpoints, or provider selection.

Validation

• parsed the full JSON example with jq and verified every model has the required fields
• loaded the extracted example with Droid CLI 0.171.0 and confirmed the custom models appear in the model list
• ran git diff --check