Function proxy_to_host 

async fn proxy_to_host(
    state: &AppState,
    host: &HostIpc,
    route: &str,
    body: Value,
) -> Result<Value, String>

POST body to /agentmux/browser/{route} on the paired host and return its parsed JSON response (the host’s own {ok, data} / {ok, error} envelope — see browser_api::types::ApiResponse).