I took another fresh copy of your site and installed it locally, where it works fine. The debug log is full of (very many) warnings from your theme, but no fatal errors, as were seen in your server logs. The issue only seems to happen on your production server. I (momentarily) switched theme to the parent Genesis theme to abstract from possible issues arising from problems with your child theme, but the product field group still didn't show.
Checking your server set-up everything looks fine in terms of available resources.
I'm at something of a dead-end and so I have asked me colleagues to step in and take over.
My colleague read through this whole thread to see if I was missing anything and visited your site to see for himself.
He notes that several times (specifically 3) you have replied that it is working, only to the update that it has stopped working.
It works without problem on my copy of your site on my local server. If you want I can upload the copy of your site to demonstrate that it works fine on our servers.
If you are not changing things yourself which could account for it working, not working, working, not working etc. then the only thing that comes to mind is that it could reflect the load on your shared servers and sometimes the server resources being inadequate. The settings look fine, but the server might fail to provide them if stressed.
I suggest you
- make a new staging version of the site with an up-to-date copy of the production server
- delete the error logs from the staging server so that you can start with clean logs in case any issues are reported
- verify whether or not the product field group works on the staging site
- if they do then you should be speaking to your host about why the same site doesn't work in production
- if they don't then you should go through basic steps to try and pin-point the issue (bearing mind that the problem only exists on your servers, I can't reproduce it on mine), such as checking the error logs, testing for conflicts by changing theme and disabling other plugins
- WP Engine is a very controlled environment, and the key difference between your site on their servers and on my local server is that they include several Must Use plugins, which I must de-activate on my server as they won't work.
If you (or the client) have not been doing anything to account for why it sometimes works and at other times does not, I suspect server stress to be the most likely cause, and WP Engine should be able to provide more info about that.
Sorry to barge in on this. But I have similar issues. "Post fields to be shown as columns in Post Types listing in WordPress Admin" are not showing when I edit or add a new post. And I have no WooCommerce installed. I deactivated all plugins and switched to a default theme, I deleted caches, activated only toolset etc. but I don't see the Post Fields. This behavior happens with Types 3.0 and 3.0.1. but not with Types 2.3.3. And it happens before and after running the migration (relationships).
Further installed Toolset plugins: Layouts 2.3.1 and Views 2.6.1 (<- both without problems together with Types 2.3.3)
Theme Genesis (but a default theme makes no difference).
PHP Version 7.2.5.
The existing values of the missing Post Fields are visible in Front End.
I don't expect, that you respond here to my issue. I will keep reading this thread and hopefully my additional informations will help to solve both issues.