fix: preserve unmanaged Claude settings on switch

[KiBlazer]

Summary

• Preserve unmanaged fields in ~/.claude/settings.json when switching Claude providers.
• Keep provider-owned Claude env keys managed by cc-switch-cli, removing stale provider values during live writes.
• Prevent live-only Claude settings from being backfilled into provider snapshots.

Test Plan

• cargo fmt --check
• cargo test --lib
• Real switch test: chatgpt-ep -> chatgpt-k1587-163 -> chatgpt-ep
  • verified custom live-only test fields were preserved
  • verified provider-owned ANTHROPIC_* values switched correctly
  • verified exported provider snapshot did not include live-only test fields

[SaladDay]

感谢你提交这个修复，方向是很有价值的 👍

我这边看了一下，有几个地方需要再调整一下：

1. 现在 PR 和最新 main 有冲突，尤其是 config.toml信任的文件夹和配置在下次切换回来的时候就自动覆盖消失 #123 fix(provider): unify common config live handling 已经重构了 common config 的写入/剥离语义，需要先 rebase 到最新 main 后重新处理冲突。
2. 需要尽量复用当前 main 里的 common_config::* 统一逻辑，不要回退到旧的 Claude-only merge/strip 路径。特别是 common config 的 precedence 现在已经语义调整过。
3. “保留 unmanaged live settings” 这个思路是对的，但建议把它做成 Claude live write 外层的窄修复：只保护 statusLine、permissions 等 Claude 用户配置，同时继续让 cc-switch 管理 provider-owned 的 ANTHROPIC_* 字段。