Healthcheck appears to not be using the custom `CODEX_HOME` and path binary settings

[adelrodriguez]

I have a custom CODEX_HOME at .config/codex, so I updated the settings. While the app works fine, I'm getting Codex CLI is not authenticated. Run `codex login` and try again. error during login. My Codex CLI is configured correctly and I can use the app with no issues, just the warning.

I went through the codebase with Claude and came up with this assessment:

The app settings expose codexBinaryPath and codexHomePath fields, and the session start logic in codexAppServerManager.ts correctly reads both — using the custom binary path to spawn codex and passing CODEX_HOME into the child process environment. However, the ProviderHealth startup health check ignores both settings entirely. checkCodexProviderStatus in ProviderHealth.ts hardcodes the binary as "codex" and passes no environment overrides. It only depends on ChildProcessSpawner — it has no access to ServerConfig or any app settings service.

I was able to (temporarily) fix it by doing launchctl setenv CODEX_HOME <path>

I'm running v0.0.9 on MacOS 26.3.

Happy to open a PR for this but it might just be a one prompt fix.