Move .claude.json config and backups into .claude/ directory

Feature Request

Currently, ~/.claude.json and its auto-generated backup/corrupted files (.claude.json.backup.*, .claude.json.corrupted.*) are stored directly in the user's home directory. Over time, the backup files accumulate and clutter the home folder.

Current Behavior

• ~/.claude.json — main config file
• ~/.claude.json.backup.<timestamp> — created on every config write
• ~/.claude.json.corrupted.<timestamp> — created on crash recovery

These pile up in ~/ with no automatic cleanup.

Proposed Solution

One or more of the following:

1. Move ~/.claude.json into ~/.claude/config.json — the .claude/ directory already exists for plugins, projects, and todos. The main config file fits naturally there.
2. Store backups inside ~/.claude/backups/ instead of alongside the config in the home directory.
3. Add an environment variable (e.g., CLAUDE_CONFIG_PATH) to let users customize the config location.
4. Auto-clean old backups — keep only the most recent 1-2 backups and delete older ones automatically.

Workaround

Currently using a Stop hook to delete backup files at session end:

{
  "type": "command",
  "command": "powershell -NoProfile -Command \"Remove-Item '$env:USERPROFILE\\.claude.json.backup.*','$env:USERPROFILE\\.claude.json.corrupted.*' -ErrorAction SilentlyContinue\"",
  "timeout": 5000
}

This works but shouldn't be necessary.

Environment

• Windows 11
• Claude Code CLI + VS Code extension