Display API rate limiting details in health check

### Feature summary

Display GitHub API rate limiting (gh api rate_limit) details in the health check

### What problem are you trying to solve?

I hit GitHub API rate limits today which completely stopped me from working completely. The GitHub status page showed everything operational, but all my sessions were blocked due to "GitHub authorization needed". The built-in health check in the app reported that authorization was good for my account, which is weird. Trying to re-authorize my account always resulted in "failed to fetch user info after auth". I rebooted, same problem. I looked at the logs, and then saw that the call to fetch user info had failed due to API rate limiting.

If API rate limiting information had been displayed in the health check, I wouldn't have wasted time chasing the wrong problem. The rate limit info also includes the time at which the rate limit resets, so it's very useful to know if I just need to take a coffee break and for how long. It would also be useful to let me see if I'm using way too much API calls when I'm not supposed to.

### Proposed solution

Simply display the output from the gh api rate_limit command in the health check, that would certainly do the trick.

### Workflow impact

Critical - it stopped all my sessions and I couldn't get anything done.

### Installation context

_No response_

### Additional context

从应用内置的健康检查开始，跟踪 GitHub 授权状态的收集方式；使用 issue 中描述的 gh api rate_limit 输出作为参考。完成的标准是健康检查在授权状态旁显示速率限制使用情况和重置时间的详细信息，使得当限制导致 GitHub 请求失败时，这些限制可见。

由索引模型根据 Issue 内容生成。