Hi @hanagroup,
Yes, you’re right the issue is your child theme does not recognize its parent x theme. It can be easily resolved by editing the child theme style.css file and change this line Template: milneinstitute to Template: x
However, this is not your biggest issue. Your biggest issue would be if these customizations you have on the child theme will cause a conflict on the latest version, so you need to audit these customizations first and see which needs to be retail and which needs to be updated to adhere to the latest version. Regretfully we can not provide support for these customizations and you need to test this on your own.
I advise you to keep the live site intact for now, and set up a staging server to clone the site, and then do the updating on the staging site first so you can troubleshoot it properly when an issue with those child themes occurs.
How to Clone a WordPress Site in 7 Easy Steps
Another thing, do not rename the x folder to something else, just keep it as x or the child theme or other dependent things won’t find it, causing unforeseen issues.
Let us know how it goes,
Cheers