[BUG] Documentation inconsistency: outputStyle setting documented but not supported

Bug Description

There is an inconsistency between the Claude Code documentation and actual functionality regarding the outputStyle setting. The output-styles documentation
page states that output style changes are "saved in .claude/settings.local.json", but attempting to add this setting results in a validation error.

Steps to Reproduce

1. Read the documentation at https://docs.anthropic.com/en/docs/claude-code/output-styles which states that output style settings are saved to

.claude/settings.local.json

1. Add "outputStyle": "detailed" to .claude/settings.local.json file
2. Attempt to use Claude Code with this setting
3. Observe validation error: "Property outputStyle is not allowed"

Expected Behavior

Either:

• The outputStyle property should be accepted in .claude/settings.local.json as documented, allowing persistent output style preferences, OR
• The documentation should be corrected to clarify that output styles are session-only and cannot be persisted in settings files

Actual Behavior

• The outputStyle property is rejected when added to settings files with validation error "Property outputStyle is not allowed"
• Output style appears to be session-only despite documentation claiming it can be saved persistently
• There's no mention of outputStyle in the settings documentation or schema validation

Environment

• OS: macOS 15.6 (24G84)
• Platform: Darwin
• Claude Code: Latest version
• Settings file: .claude/settings.local.json

Additional Context

This inconsistency creates confusion for users who expect to be able to persist their preferred output style settings based on the documentation, but
encounter validation errors when attempting to do so.

Suggested Fix

1. Option A: Update the settings schema to support outputStyle property and implement persistence functionality
2. Option B: Update the documentation to clarify that output styles are session-only and remove references to saving them in settings files