Right. I don't understand what you want me to test here. I have checked all the files in my local folder and there is nothing to create this issue.
The issue is that when installing joomla 3.9.2 over Joomla 3.8.12, the home menu (assigned to its own template) reverts to rendering the the home page through the default layout even though it is still assigned to a different template.
There is definitely something wrong with Joomla 3.9.2 or Purity. And possibly only with local files.
Telling me to test without that doesn't make sense. local is still a feature you provide. All I've done is add additional classes to the files.