[FEATURE] Support ~/.claude/settings.local.json

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

I want to save the env to ~/.claude/settings.local.json
I want to checkin ~/.claude/settings.json to my dotfiles repo that can share to multi place.

Proposed Solution

support ~/.claude/settings.local.json

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

I have multi workspace, i'd like to sync workspace easily
I want to share ~/.claude/settings.json across multi workspace
the workspace maybe just a onetime container, the i checkout the dotfiles to setup everything.

~/.claude/settings.json maybe change quickly when build custome command.

Additional Context

_No response_