The “Error Logs” panel from the “Site Info” was designed to display the logs from the main error_log file, which according to the PHP documentation will be placed either in the document root of in the parent directory (behind the document root). There is a setting that can be used to force PHP to store the logs of specific scripts in their own directories, this is why the hardening page displays more than one file in its report, because it searches across all the project to see if there are more error logs.
I do not know if it is worth the effort to modify the “Error Logs” panel to display the content of log files that are not in the document root, it would require to scan the project every time the page is loaded. I will think about this for some days, but I will probably not leave the code as is.